The influence of the coefficients of a system of wave equations coupled by velocities on its stabilization
Abstract In this work, we consider a system of two wave equations coupled by velocities in a one-dimensional space, with one boundary fractional damping. First, we show that the system is strongly asymptotically stable if and only if the coupling parameter b of the two equations is outside a discret...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Akil, Mohammad [verfasserIn] Ghader, Mouhammad [verfasserIn] Wehbe, Ali [verfasserIn] |
|---|
| Format: |
E-Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
2020 |
|---|
| Schlagwörter: |
|---|
| Anmerkung: |
© Sociedad Española de Matemática Aplicada 2020 |
|---|
| Übergeordnetes Werk: |
Enthalten in: SeMA journal - Berlin : Springer, 2010, 78(2020), 3 vom: 02. Nov., Seite 287-333 |
|---|---|
| Übergeordnetes Werk: |
volume:78 ; year:2020 ; number:3 ; day:02 ; month:11 ; pages:287-333 |
| Links: |
|---|
| DOI / URN: |
10.1007/s40324-020-00233-y |
|---|
| Katalog-ID: |
SPR044767587 |
|---|
| LEADER | 01000caa a22002652 4500 | ||
|---|---|---|---|
| 001 | SPR044767587 | ||
| 003 | DE-627 | ||
| 005 | 20220112030112.0 | ||
| 007 | cr uuu---uuuuu | ||
| 008 | 210807s2020 xx |||||o 00| ||eng c | ||
| 024 | 7 | |a 10.1007/s40324-020-00233-y |2 doi | |
| 035 | |a (DE-627)SPR044767587 | ||
| 035 | |a (SPR)s40324-020-00233-y-e | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rakwb | ||
| 041 | |a eng | ||
| 082 | 0 | 4 | |a 510 |q ASE |
| 100 | 1 | |a Akil, Mohammad |e verfasserin |4 aut | |
| 245 | 1 | 4 | |a The influence of the coefficients of a system of wave equations coupled by velocities on its stabilization |
| 264 | 1 | |c 2020 | |
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a Computermedien |b c |2 rdamedia | ||
| 338 | |a Online-Ressource |b cr |2 rdacarrier | ||
| 500 | |a © Sociedad Española de Matemática Aplicada 2020 | ||
| 520 | |a Abstract In this work, we consider a system of two wave equations coupled by velocities in a one-dimensional space, with one boundary fractional damping. First, we show that the system is strongly asymptotically stable if and only if the coupling parameter b of the two equations is outside a discrete set of exceptional real values. Next, we show that our system is not uniformly stable. Hence, we look for a polynomial decay rate for smooth initial data. Using a frequency domain approach combined with the multiplier method, we prove that the energy decay rate is greatly influenced by the nature of the coupling parameter b, the arithmetic property of the wave propagation speed a and the order of the fractional damping %$\alpha %$. Indeed, under the equal speed propagation condition, i.e., %$a=1%$, we establish an optimal polynomial energy decay rate of type %$t^{-\frac{2}{{1-\alpha }}}%$ if the coupling parameter %$b\notin \pi {\mathbb {Z}}%$ and of type %$t^{-\frac{2}{{5-\alpha }}}%$ if the coupling parameter %$b\in \pi {\mathbb {Z}}%$. Furthermore, when the wave propagates with different speeds, i.e., %$a\not =1%$, we prove that, for any rational number %$\sqrt{a}%$ and almost all irrational numbers %$\sqrt{a}%$, the energy of our system decays polynomially to zero like as %$t^{-\frac{2}{{5-\alpha }}}%$. This result still holds if %$a\in {\mathbb {Q}}%$, %$\sqrt{a}\notin {\mathbb {Q}}%$ and b small enough. | ||
| 650 | 4 | |a Coupled wave equations |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Fractional boundary damping |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Strong stability |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Uniform stability |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Polynomial stability |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Ghader, Mouhammad |e verfasserin |4 aut | |
| 700 | 1 | |a Wehbe, Ali |e verfasserin |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t SeMA journal |d Berlin : Springer, 2010 |g 78(2020), 3 vom: 02. Nov., Seite 287-333 |w (DE-627)815395299 |w (DE-600)2805493-3 |x 2254-3902 |7 nnns |
| 773 | 1 | 8 | |g volume:78 |g year:2020 |g number:3 |g day:02 |g month:11 |g pages:287-333 |
| 856 | 4 | 0 | |u https://dx.doi.org/10.1007/s40324-020-00233-y |z lizenzpflichtig |3 Volltext |
| 912 | |a GBV_USEFLAG_A | ||
| 912 | |a SYSFLAG_A | ||
| 912 | |a GBV_SPRINGER | ||
| 912 | |a GBV_ILN_11 | ||
| 912 | |a GBV_ILN_20 | ||
| 912 | |a GBV_ILN_22 | ||
| 912 | |a GBV_ILN_23 | ||
| 912 | |a GBV_ILN_24 | ||
| 912 | |a GBV_ILN_31 | ||
| 912 | |a GBV_ILN_32 | ||
| 912 | |a GBV_ILN_39 | ||
| 912 | |a GBV_ILN_40 | ||
| 912 | |a GBV_ILN_60 | ||
| 912 | |a GBV_ILN_62 | ||
| 912 | |a GBV_ILN_63 | ||
| 912 | |a GBV_ILN_65 | ||
| 912 | |a GBV_ILN_69 | ||
| 912 | |a GBV_ILN_70 | ||
| 912 | |a GBV_ILN_73 | ||
| 912 | |a GBV_ILN_74 | ||
| 912 | |a GBV_ILN_90 | ||
| 912 | |a GBV_ILN_95 | ||
| 912 | |a GBV_ILN_100 | ||
| 912 | |a GBV_ILN_105 | ||
| 912 | |a GBV_ILN_110 | ||
| 912 | |a GBV_ILN_120 | ||
| 912 | |a GBV_ILN_138 | ||
| 912 | |a GBV_ILN_150 | ||
| 912 | |a GBV_ILN_151 | ||
| 912 | |a GBV_ILN_152 | ||
| 912 | |a GBV_ILN_161 | ||
| 912 | |a GBV_ILN_170 | ||
| 912 | |a GBV_ILN_171 | ||
| 912 | |a GBV_ILN_187 | ||
| 912 | |a GBV_ILN_213 | ||
| 912 | |a GBV_ILN_224 | ||
| 912 | |a GBV_ILN_230 | ||
| 912 | |a GBV_ILN_250 | ||
| 912 | |a GBV_ILN_281 | ||
| 912 | |a GBV_ILN_285 | ||
| 912 | |a GBV_ILN_293 | ||
| 912 | |a GBV_ILN_370 | ||
| 912 | |a GBV_ILN_602 | ||
| 912 | |a GBV_ILN_636 | ||
| 912 | |a GBV_ILN_702 | ||
| 912 | |a GBV_ILN_2001 | ||
| 912 | |a GBV_ILN_2003 | ||
| 912 | |a GBV_ILN_2004 | ||
| 912 | |a GBV_ILN_2005 | ||
| 912 | |a GBV_ILN_2006 | ||
| 912 | |a GBV_ILN_2007 | ||
| 912 | |a GBV_ILN_2008 | ||
| 912 | |a GBV_ILN_2009 | ||
| 912 | |a GBV_ILN_2010 | ||
| 912 | |a GBV_ILN_2011 | ||
| 912 | |a GBV_ILN_2014 | ||
| 912 | |a GBV_ILN_2015 | ||
| 912 | |a GBV_ILN_2018 | ||
| 912 | |a GBV_ILN_2020 | ||
| 912 | |a GBV_ILN_2021 | ||
| 912 | |a GBV_ILN_2025 | ||
| 912 | |a GBV_ILN_2026 | ||
| 912 | |a GBV_ILN_2027 | ||
| 912 | |a GBV_ILN_2031 | ||
| 912 | |a GBV_ILN_2034 | ||
| 912 | |a GBV_ILN_2037 | ||
| 912 | |a GBV_ILN_2038 | ||
| 912 | |a GBV_ILN_2039 | ||
| 912 | |a GBV_ILN_2044 | ||
| 912 | |a GBV_ILN_2048 | ||
| 912 | |a GBV_ILN_2049 | ||
| 912 | |a GBV_ILN_2050 | ||
| 912 | |a GBV_ILN_2055 | ||
| 912 | |a GBV_ILN_2056 | ||
| 912 | |a GBV_ILN_2057 | ||
| 912 | |a GBV_ILN_2059 | ||
| 912 | |a GBV_ILN_2061 | ||
| 912 | |a GBV_ILN_2064 | ||
| 912 | |a GBV_ILN_2065 | ||
| 912 | |a GBV_ILN_2068 | ||
| 912 | |a GBV_ILN_2088 | ||
| 912 | |a GBV_ILN_2093 | ||
| 912 | |a GBV_ILN_2106 | ||
| 912 | |a GBV_ILN_2107 | ||
| 912 | |a GBV_ILN_2108 | ||
| 912 | |a GBV_ILN_2110 | ||
| 912 | |a GBV_ILN_2111 | ||
| 912 | |a GBV_ILN_2112 | ||
| 912 | |a GBV_ILN_2113 | ||
| 912 | |a GBV_ILN_2118 | ||
| 912 | |a GBV_ILN_2122 | ||
| 912 | |a GBV_ILN_2129 | ||
| 912 | |a GBV_ILN_2143 | ||
| 912 | |a GBV_ILN_2144 | ||
| 912 | |a GBV_ILN_2147 | ||
| 912 | |a GBV_ILN_2148 | ||
| 912 | |a GBV_ILN_2152 | ||
| 912 | |a GBV_ILN_2153 | ||
| 912 | |a GBV_ILN_2188 | ||
| 912 | |a GBV_ILN_2190 | ||
| 912 | |a GBV_ILN_2232 | ||
| 912 | |a GBV_ILN_2336 | ||
| 912 | |a GBV_ILN_2446 | ||
| 912 | |a GBV_ILN_2470 | ||
| 912 | |a GBV_ILN_2472 | ||
| 912 | |a GBV_ILN_2507 | ||
| 912 | |a GBV_ILN_2522 | ||
| 912 | |a GBV_ILN_2548 | ||
| 912 | |a GBV_ILN_4035 | ||
| 912 | |a GBV_ILN_4037 | ||
| 912 | |a GBV_ILN_4046 | ||
| 912 | |a GBV_ILN_4112 | ||
| 912 | |a GBV_ILN_4125 | ||
| 912 | |a GBV_ILN_4126 | ||
| 912 | |a GBV_ILN_4242 | ||
| 912 | |a GBV_ILN_4246 | ||
| 912 | |a GBV_ILN_4249 | ||
| 912 | |a GBV_ILN_4251 | ||
| 912 | |a GBV_ILN_4305 | ||
| 912 | |a GBV_ILN_4306 | ||
| 912 | |a GBV_ILN_4307 | ||
| 912 | |a GBV_ILN_4313 | ||
| 912 | |a GBV_ILN_4322 | ||
| 912 | |a GBV_ILN_4323 | ||
| 912 | |a GBV_ILN_4324 | ||
| 912 | |a GBV_ILN_4325 | ||
| 912 | |a GBV_ILN_4326 | ||
| 912 | |a GBV_ILN_4328 | ||
| 912 | |a GBV_ILN_4333 | ||
| 912 | |a GBV_ILN_4334 | ||
| 912 | |a GBV_ILN_4335 | ||
| 912 | |a GBV_ILN_4336 | ||
| 912 | |a GBV_ILN_4338 | ||
| 912 | |a GBV_ILN_4393 | ||
| 912 | |a GBV_ILN_4700 | ||
| 951 | |a AR | ||
| 952 | |d 78 |j 2020 |e 3 |b 02 |c 11 |h 287-333 | ||
| author_variant |
m a ma m g mg a w aw |
|---|---|
| matchkey_str |
article:22543902:2020----::hifunefhcefcetoaytmfaeqainculdyeo |
| hierarchy_sort_str |
2020 |
| publishDate |
2020 |
| allfields |
10.1007/s40324-020-00233-y doi (DE-627)SPR044767587 (SPR)s40324-020-00233-y-e DE-627 ger DE-627 rakwb eng 510 ASE Akil, Mohammad verfasserin aut The influence of the coefficients of a system of wave equations coupled by velocities on its stabilization 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Sociedad Española de Matemática Aplicada 2020 Abstract In this work, we consider a system of two wave equations coupled by velocities in a one-dimensional space, with one boundary fractional damping. First, we show that the system is strongly asymptotically stable if and only if the coupling parameter b of the two equations is outside a discrete set of exceptional real values. Next, we show that our system is not uniformly stable. Hence, we look for a polynomial decay rate for smooth initial data. Using a frequency domain approach combined with the multiplier method, we prove that the energy decay rate is greatly influenced by the nature of the coupling parameter b, the arithmetic property of the wave propagation speed a and the order of the fractional damping %$\alpha %$. Indeed, under the equal speed propagation condition, i.e., %$a=1%$, we establish an optimal polynomial energy decay rate of type %$t^{-\frac{2}{{1-\alpha }}}%$ if the coupling parameter %$b\notin \pi {\mathbb {Z}}%$ and of type %$t^{-\frac{2}{{5-\alpha }}}%$ if the coupling parameter %$b\in \pi {\mathbb {Z}}%$. Furthermore, when the wave propagates with different speeds, i.e., %$a\not =1%$, we prove that, for any rational number %$\sqrt{a}%$ and almost all irrational numbers %$\sqrt{a}%$, the energy of our system decays polynomially to zero like as %$t^{-\frac{2}{{5-\alpha }}}%$. This result still holds if %$a\in {\mathbb {Q}}%$, %$\sqrt{a}\notin {\mathbb {Q}}%$ and b small enough. Coupled wave equations (dpeaa)DE-He213 Fractional boundary damping (dpeaa)DE-He213 Strong stability (dpeaa)DE-He213 Uniform stability (dpeaa)DE-He213 Polynomial stability (dpeaa)DE-He213 Ghader, Mouhammad verfasserin aut Wehbe, Ali verfasserin aut Enthalten in SeMA journal Berlin : Springer, 2010 78(2020), 3 vom: 02. Nov., Seite 287-333 (DE-627)815395299 (DE-600)2805493-3 2254-3902 nnns volume:78 year:2020 number:3 day:02 month:11 pages:287-333 https://dx.doi.org/10.1007/s40324-020-00233-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 78 2020 3 02 11 287-333 |
| spelling |
10.1007/s40324-020-00233-y doi (DE-627)SPR044767587 (SPR)s40324-020-00233-y-e DE-627 ger DE-627 rakwb eng 510 ASE Akil, Mohammad verfasserin aut The influence of the coefficients of a system of wave equations coupled by velocities on its stabilization 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Sociedad Española de Matemática Aplicada 2020 Abstract In this work, we consider a system of two wave equations coupled by velocities in a one-dimensional space, with one boundary fractional damping. First, we show that the system is strongly asymptotically stable if and only if the coupling parameter b of the two equations is outside a discrete set of exceptional real values. Next, we show that our system is not uniformly stable. Hence, we look for a polynomial decay rate for smooth initial data. Using a frequency domain approach combined with the multiplier method, we prove that the energy decay rate is greatly influenced by the nature of the coupling parameter b, the arithmetic property of the wave propagation speed a and the order of the fractional damping %$\alpha %$. Indeed, under the equal speed propagation condition, i.e., %$a=1%$, we establish an optimal polynomial energy decay rate of type %$t^{-\frac{2}{{1-\alpha }}}%$ if the coupling parameter %$b\notin \pi {\mathbb {Z}}%$ and of type %$t^{-\frac{2}{{5-\alpha }}}%$ if the coupling parameter %$b\in \pi {\mathbb {Z}}%$. Furthermore, when the wave propagates with different speeds, i.e., %$a\not =1%$, we prove that, for any rational number %$\sqrt{a}%$ and almost all irrational numbers %$\sqrt{a}%$, the energy of our system decays polynomially to zero like as %$t^{-\frac{2}{{5-\alpha }}}%$. This result still holds if %$a\in {\mathbb {Q}}%$, %$\sqrt{a}\notin {\mathbb {Q}}%$ and b small enough. Coupled wave equations (dpeaa)DE-He213 Fractional boundary damping (dpeaa)DE-He213 Strong stability (dpeaa)DE-He213 Uniform stability (dpeaa)DE-He213 Polynomial stability (dpeaa)DE-He213 Ghader, Mouhammad verfasserin aut Wehbe, Ali verfasserin aut Enthalten in SeMA journal Berlin : Springer, 2010 78(2020), 3 vom: 02. Nov., Seite 287-333 (DE-627)815395299 (DE-600)2805493-3 2254-3902 nnns volume:78 year:2020 number:3 day:02 month:11 pages:287-333 https://dx.doi.org/10.1007/s40324-020-00233-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 78 2020 3 02 11 287-333 |
| allfields_unstemmed |
10.1007/s40324-020-00233-y doi (DE-627)SPR044767587 (SPR)s40324-020-00233-y-e DE-627 ger DE-627 rakwb eng 510 ASE Akil, Mohammad verfasserin aut The influence of the coefficients of a system of wave equations coupled by velocities on its stabilization 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Sociedad Española de Matemática Aplicada 2020 Abstract In this work, we consider a system of two wave equations coupled by velocities in a one-dimensional space, with one boundary fractional damping. First, we show that the system is strongly asymptotically stable if and only if the coupling parameter b of the two equations is outside a discrete set of exceptional real values. Next, we show that our system is not uniformly stable. Hence, we look for a polynomial decay rate for smooth initial data. Using a frequency domain approach combined with the multiplier method, we prove that the energy decay rate is greatly influenced by the nature of the coupling parameter b, the arithmetic property of the wave propagation speed a and the order of the fractional damping %$\alpha %$. Indeed, under the equal speed propagation condition, i.e., %$a=1%$, we establish an optimal polynomial energy decay rate of type %$t^{-\frac{2}{{1-\alpha }}}%$ if the coupling parameter %$b\notin \pi {\mathbb {Z}}%$ and of type %$t^{-\frac{2}{{5-\alpha }}}%$ if the coupling parameter %$b\in \pi {\mathbb {Z}}%$. Furthermore, when the wave propagates with different speeds, i.e., %$a\not =1%$, we prove that, for any rational number %$\sqrt{a}%$ and almost all irrational numbers %$\sqrt{a}%$, the energy of our system decays polynomially to zero like as %$t^{-\frac{2}{{5-\alpha }}}%$. This result still holds if %$a\in {\mathbb {Q}}%$, %$\sqrt{a}\notin {\mathbb {Q}}%$ and b small enough. Coupled wave equations (dpeaa)DE-He213 Fractional boundary damping (dpeaa)DE-He213 Strong stability (dpeaa)DE-He213 Uniform stability (dpeaa)DE-He213 Polynomial stability (dpeaa)DE-He213 Ghader, Mouhammad verfasserin aut Wehbe, Ali verfasserin aut Enthalten in SeMA journal Berlin : Springer, 2010 78(2020), 3 vom: 02. Nov., Seite 287-333 (DE-627)815395299 (DE-600)2805493-3 2254-3902 nnns volume:78 year:2020 number:3 day:02 month:11 pages:287-333 https://dx.doi.org/10.1007/s40324-020-00233-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 78 2020 3 02 11 287-333 |
| allfieldsGer |
10.1007/s40324-020-00233-y doi (DE-627)SPR044767587 (SPR)s40324-020-00233-y-e DE-627 ger DE-627 rakwb eng 510 ASE Akil, Mohammad verfasserin aut The influence of the coefficients of a system of wave equations coupled by velocities on its stabilization 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Sociedad Española de Matemática Aplicada 2020 Abstract In this work, we consider a system of two wave equations coupled by velocities in a one-dimensional space, with one boundary fractional damping. First, we show that the system is strongly asymptotically stable if and only if the coupling parameter b of the two equations is outside a discrete set of exceptional real values. Next, we show that our system is not uniformly stable. Hence, we look for a polynomial decay rate for smooth initial data. Using a frequency domain approach combined with the multiplier method, we prove that the energy decay rate is greatly influenced by the nature of the coupling parameter b, the arithmetic property of the wave propagation speed a and the order of the fractional damping %$\alpha %$. Indeed, under the equal speed propagation condition, i.e., %$a=1%$, we establish an optimal polynomial energy decay rate of type %$t^{-\frac{2}{{1-\alpha }}}%$ if the coupling parameter %$b\notin \pi {\mathbb {Z}}%$ and of type %$t^{-\frac{2}{{5-\alpha }}}%$ if the coupling parameter %$b\in \pi {\mathbb {Z}}%$. Furthermore, when the wave propagates with different speeds, i.e., %$a\not =1%$, we prove that, for any rational number %$\sqrt{a}%$ and almost all irrational numbers %$\sqrt{a}%$, the energy of our system decays polynomially to zero like as %$t^{-\frac{2}{{5-\alpha }}}%$. This result still holds if %$a\in {\mathbb {Q}}%$, %$\sqrt{a}\notin {\mathbb {Q}}%$ and b small enough. Coupled wave equations (dpeaa)DE-He213 Fractional boundary damping (dpeaa)DE-He213 Strong stability (dpeaa)DE-He213 Uniform stability (dpeaa)DE-He213 Polynomial stability (dpeaa)DE-He213 Ghader, Mouhammad verfasserin aut Wehbe, Ali verfasserin aut Enthalten in SeMA journal Berlin : Springer, 2010 78(2020), 3 vom: 02. Nov., Seite 287-333 (DE-627)815395299 (DE-600)2805493-3 2254-3902 nnns volume:78 year:2020 number:3 day:02 month:11 pages:287-333 https://dx.doi.org/10.1007/s40324-020-00233-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 78 2020 3 02 11 287-333 |
| allfieldsSound |
10.1007/s40324-020-00233-y doi (DE-627)SPR044767587 (SPR)s40324-020-00233-y-e DE-627 ger DE-627 rakwb eng 510 ASE Akil, Mohammad verfasserin aut The influence of the coefficients of a system of wave equations coupled by velocities on its stabilization 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Sociedad Española de Matemática Aplicada 2020 Abstract In this work, we consider a system of two wave equations coupled by velocities in a one-dimensional space, with one boundary fractional damping. First, we show that the system is strongly asymptotically stable if and only if the coupling parameter b of the two equations is outside a discrete set of exceptional real values. Next, we show that our system is not uniformly stable. Hence, we look for a polynomial decay rate for smooth initial data. Using a frequency domain approach combined with the multiplier method, we prove that the energy decay rate is greatly influenced by the nature of the coupling parameter b, the arithmetic property of the wave propagation speed a and the order of the fractional damping %$\alpha %$. Indeed, under the equal speed propagation condition, i.e., %$a=1%$, we establish an optimal polynomial energy decay rate of type %$t^{-\frac{2}{{1-\alpha }}}%$ if the coupling parameter %$b\notin \pi {\mathbb {Z}}%$ and of type %$t^{-\frac{2}{{5-\alpha }}}%$ if the coupling parameter %$b\in \pi {\mathbb {Z}}%$. Furthermore, when the wave propagates with different speeds, i.e., %$a\not =1%$, we prove that, for any rational number %$\sqrt{a}%$ and almost all irrational numbers %$\sqrt{a}%$, the energy of our system decays polynomially to zero like as %$t^{-\frac{2}{{5-\alpha }}}%$. This result still holds if %$a\in {\mathbb {Q}}%$, %$\sqrt{a}\notin {\mathbb {Q}}%$ and b small enough. Coupled wave equations (dpeaa)DE-He213 Fractional boundary damping (dpeaa)DE-He213 Strong stability (dpeaa)DE-He213 Uniform stability (dpeaa)DE-He213 Polynomial stability (dpeaa)DE-He213 Ghader, Mouhammad verfasserin aut Wehbe, Ali verfasserin aut Enthalten in SeMA journal Berlin : Springer, 2010 78(2020), 3 vom: 02. Nov., Seite 287-333 (DE-627)815395299 (DE-600)2805493-3 2254-3902 nnns volume:78 year:2020 number:3 day:02 month:11 pages:287-333 https://dx.doi.org/10.1007/s40324-020-00233-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 78 2020 3 02 11 287-333 |
| language |
English |
| source |
Enthalten in SeMA journal 78(2020), 3 vom: 02. Nov., Seite 287-333 volume:78 year:2020 number:3 day:02 month:11 pages:287-333 |
| sourceStr |
Enthalten in SeMA journal 78(2020), 3 vom: 02. Nov., Seite 287-333 volume:78 year:2020 number:3 day:02 month:11 pages:287-333 |
| format_phy_str_mv |
Article |
| institution |
findex.gbv.de |
| topic_facet |
Coupled wave equations Fractional boundary damping Strong stability Uniform stability Polynomial stability |
| dewey-raw |
510 |
| isfreeaccess_bool |
false |
| container_title |
SeMA journal |
| authorswithroles_txt_mv |
Akil, Mohammad @@aut@@ Ghader, Mouhammad @@aut@@ Wehbe, Ali @@aut@@ |
| publishDateDaySort_date |
2020-11-02T00:00:00Z |
| hierarchy_top_id |
815395299 |
| dewey-sort |
3510 |
| id |
SPR044767587 |
| language_de |
englisch |
| fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR044767587</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20220112030112.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">210807s2020 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s40324-020-00233-y</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR044767587</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s40324-020-00233-y-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">ASE</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Akil, Mohammad</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="4"><subfield code="a">The influence of the coefficients of a system of wave equations coupled by velocities on its stabilization</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2020</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Sociedad Española de Matemática Aplicada 2020</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract In this work, we consider a system of two wave equations coupled by velocities in a one-dimensional space, with one boundary fractional damping. First, we show that the system is strongly asymptotically stable if and only if the coupling parameter b of the two equations is outside a discrete set of exceptional real values. Next, we show that our system is not uniformly stable. Hence, we look for a polynomial decay rate for smooth initial data. Using a frequency domain approach combined with the multiplier method, we prove that the energy decay rate is greatly influenced by the nature of the coupling parameter b, the arithmetic property of the wave propagation speed a and the order of the fractional damping %$\alpha %$. Indeed, under the equal speed propagation condition, i.e., %$a=1%$, we establish an optimal polynomial energy decay rate of type %$t^{-\frac{2}{{1-\alpha }}}%$ if the coupling parameter %$b\notin \pi {\mathbb {Z}}%$ and of type %$t^{-\frac{2}{{5-\alpha }}}%$ if the coupling parameter %$b\in \pi {\mathbb {Z}}%$. Furthermore, when the wave propagates with different speeds, i.e., %$a\not =1%$, we prove that, for any rational number %$\sqrt{a}%$ and almost all irrational numbers %$\sqrt{a}%$, the energy of our system decays polynomially to zero like as %$t^{-\frac{2}{{5-\alpha }}}%$. This result still holds if %$a\in {\mathbb {Q}}%$, %$\sqrt{a}\notin {\mathbb {Q}}%$ and b small enough.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Coupled wave equations</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fractional boundary damping</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Strong stability</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Uniform stability</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Polynomial stability</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Ghader, Mouhammad</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Wehbe, Ali</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">SeMA journal</subfield><subfield code="d">Berlin : Springer, 2010</subfield><subfield code="g">78(2020), 3 vom: 02. Nov., Seite 287-333</subfield><subfield code="w">(DE-627)815395299</subfield><subfield code="w">(DE-600)2805493-3</subfield><subfield code="x">2254-3902</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:78</subfield><subfield code="g">year:2020</subfield><subfield code="g">number:3</subfield><subfield code="g">day:02</subfield><subfield code="g">month:11</subfield><subfield code="g">pages:287-333</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1007/s40324-020-00233-y</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_SPRINGER</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_11</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_20</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_22</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_23</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_24</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_31</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_32</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_39</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_40</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_60</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_62</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_63</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_65</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_69</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_73</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_74</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_90</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_95</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_100</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_105</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_110</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_120</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_138</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_150</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_151</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_152</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_161</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_170</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_171</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_187</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_213</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_224</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_230</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_250</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_281</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_285</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_293</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_370</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_602</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_636</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_702</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2001</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2003</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2004</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2005</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2006</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2007</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2008</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2009</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2010</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2011</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2014</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2015</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2018</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2020</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2021</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2025</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2026</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2027</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2031</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2034</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2037</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2038</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2039</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2044</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2048</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2049</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2050</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2055</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2056</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2057</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2059</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2061</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2064</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2065</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2068</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2088</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2093</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2106</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2107</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2108</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2110</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2111</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2112</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2113</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2118</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2122</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2129</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2143</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2144</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2147</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2148</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2152</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2153</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2188</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2190</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2232</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2336</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2446</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2470</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2472</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2507</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2522</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2548</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4035</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4037</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4046</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4112</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4125</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4126</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4242</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4246</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4249</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4251</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4305</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4306</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4307</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4313</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4322</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4323</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4324</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4325</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4326</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4328</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4333</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4334</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4335</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4336</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4338</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4393</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4700</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">78</subfield><subfield code="j">2020</subfield><subfield code="e">3</subfield><subfield code="b">02</subfield><subfield code="c">11</subfield><subfield code="h">287-333</subfield></datafield></record></collection>
|
| author |
Akil, Mohammad |
| spellingShingle |
Akil, Mohammad ddc 510 misc Coupled wave equations misc Fractional boundary damping misc Strong stability misc Uniform stability misc Polynomial stability The influence of the coefficients of a system of wave equations coupled by velocities on its stabilization |
| authorStr |
Akil, Mohammad |
| ppnlink_with_tag_str_mv |
@@773@@(DE-627)815395299 |
| format |
electronic Article |
| dewey-ones |
510 - Mathematics |
| delete_txt_mv |
keep |
| author_role |
aut aut aut |
| collection |
springer |
| remote_str |
true |
| illustrated |
Not Illustrated |
| issn |
2254-3902 |
| topic_title |
510 ASE The influence of the coefficients of a system of wave equations coupled by velocities on its stabilization Coupled wave equations (dpeaa)DE-He213 Fractional boundary damping (dpeaa)DE-He213 Strong stability (dpeaa)DE-He213 Uniform stability (dpeaa)DE-He213 Polynomial stability (dpeaa)DE-He213 |
| topic |
ddc 510 misc Coupled wave equations misc Fractional boundary damping misc Strong stability misc Uniform stability misc Polynomial stability |
| topic_unstemmed |
ddc 510 misc Coupled wave equations misc Fractional boundary damping misc Strong stability misc Uniform stability misc Polynomial stability |
| topic_browse |
ddc 510 misc Coupled wave equations misc Fractional boundary damping misc Strong stability misc Uniform stability misc Polynomial stability |
| format_facet |
Elektronische Aufsätze Aufsätze Elektronische Ressource |
| format_main_str_mv |
Text Zeitschrift/Artikel |
| carriertype_str_mv |
cr |
| hierarchy_parent_title |
SeMA journal |
| hierarchy_parent_id |
815395299 |
| dewey-tens |
510 - Mathematics |
| hierarchy_top_title |
SeMA journal |
| isfreeaccess_txt |
false |
| familylinks_str_mv |
(DE-627)815395299 (DE-600)2805493-3 |
| title |
The influence of the coefficients of a system of wave equations coupled by velocities on its stabilization |
| ctrlnum |
(DE-627)SPR044767587 (SPR)s40324-020-00233-y-e |
| title_full |
The influence of the coefficients of a system of wave equations coupled by velocities on its stabilization |
| author_sort |
Akil, Mohammad |
| journal |
SeMA journal |
| journalStr |
SeMA journal |
| lang_code |
eng |
| isOA_bool |
false |
| dewey-hundreds |
500 - Science |
| recordtype |
marc |
| publishDateSort |
2020 |
| contenttype_str_mv |
txt |
| container_start_page |
287 |
| author_browse |
Akil, Mohammad Ghader, Mouhammad Wehbe, Ali |
| container_volume |
78 |
| class |
510 ASE |
| format_se |
Elektronische Aufsätze |
| author-letter |
Akil, Mohammad |
| doi_str_mv |
10.1007/s40324-020-00233-y |
| dewey-full |
510 |
| author2-role |
verfasserin |
| title_sort |
influence of the coefficients of a system of wave equations coupled by velocities on its stabilization |
| title_auth |
The influence of the coefficients of a system of wave equations coupled by velocities on its stabilization |
| abstract |
Abstract In this work, we consider a system of two wave equations coupled by velocities in a one-dimensional space, with one boundary fractional damping. First, we show that the system is strongly asymptotically stable if and only if the coupling parameter b of the two equations is outside a discrete set of exceptional real values. Next, we show that our system is not uniformly stable. Hence, we look for a polynomial decay rate for smooth initial data. Using a frequency domain approach combined with the multiplier method, we prove that the energy decay rate is greatly influenced by the nature of the coupling parameter b, the arithmetic property of the wave propagation speed a and the order of the fractional damping %$\alpha %$. Indeed, under the equal speed propagation condition, i.e., %$a=1%$, we establish an optimal polynomial energy decay rate of type %$t^{-\frac{2}{{1-\alpha }}}%$ if the coupling parameter %$b\notin \pi {\mathbb {Z}}%$ and of type %$t^{-\frac{2}{{5-\alpha }}}%$ if the coupling parameter %$b\in \pi {\mathbb {Z}}%$. Furthermore, when the wave propagates with different speeds, i.e., %$a\not =1%$, we prove that, for any rational number %$\sqrt{a}%$ and almost all irrational numbers %$\sqrt{a}%$, the energy of our system decays polynomially to zero like as %$t^{-\frac{2}{{5-\alpha }}}%$. This result still holds if %$a\in {\mathbb {Q}}%$, %$\sqrt{a}\notin {\mathbb {Q}}%$ and b small enough. © Sociedad Española de Matemática Aplicada 2020 |
| abstractGer |
Abstract In this work, we consider a system of two wave equations coupled by velocities in a one-dimensional space, with one boundary fractional damping. First, we show that the system is strongly asymptotically stable if and only if the coupling parameter b of the two equations is outside a discrete set of exceptional real values. Next, we show that our system is not uniformly stable. Hence, we look for a polynomial decay rate for smooth initial data. Using a frequency domain approach combined with the multiplier method, we prove that the energy decay rate is greatly influenced by the nature of the coupling parameter b, the arithmetic property of the wave propagation speed a and the order of the fractional damping %$\alpha %$. Indeed, under the equal speed propagation condition, i.e., %$a=1%$, we establish an optimal polynomial energy decay rate of type %$t^{-\frac{2}{{1-\alpha }}}%$ if the coupling parameter %$b\notin \pi {\mathbb {Z}}%$ and of type %$t^{-\frac{2}{{5-\alpha }}}%$ if the coupling parameter %$b\in \pi {\mathbb {Z}}%$. Furthermore, when the wave propagates with different speeds, i.e., %$a\not =1%$, we prove that, for any rational number %$\sqrt{a}%$ and almost all irrational numbers %$\sqrt{a}%$, the energy of our system decays polynomially to zero like as %$t^{-\frac{2}{{5-\alpha }}}%$. This result still holds if %$a\in {\mathbb {Q}}%$, %$\sqrt{a}\notin {\mathbb {Q}}%$ and b small enough. © Sociedad Española de Matemática Aplicada 2020 |
| abstract_unstemmed |
Abstract In this work, we consider a system of two wave equations coupled by velocities in a one-dimensional space, with one boundary fractional damping. First, we show that the system is strongly asymptotically stable if and only if the coupling parameter b of the two equations is outside a discrete set of exceptional real values. Next, we show that our system is not uniformly stable. Hence, we look for a polynomial decay rate for smooth initial data. Using a frequency domain approach combined with the multiplier method, we prove that the energy decay rate is greatly influenced by the nature of the coupling parameter b, the arithmetic property of the wave propagation speed a and the order of the fractional damping %$\alpha %$. Indeed, under the equal speed propagation condition, i.e., %$a=1%$, we establish an optimal polynomial energy decay rate of type %$t^{-\frac{2}{{1-\alpha }}}%$ if the coupling parameter %$b\notin \pi {\mathbb {Z}}%$ and of type %$t^{-\frac{2}{{5-\alpha }}}%$ if the coupling parameter %$b\in \pi {\mathbb {Z}}%$. Furthermore, when the wave propagates with different speeds, i.e., %$a\not =1%$, we prove that, for any rational number %$\sqrt{a}%$ and almost all irrational numbers %$\sqrt{a}%$, the energy of our system decays polynomially to zero like as %$t^{-\frac{2}{{5-\alpha }}}%$. This result still holds if %$a\in {\mathbb {Q}}%$, %$\sqrt{a}\notin {\mathbb {Q}}%$ and b small enough. © Sociedad Española de Matemática Aplicada 2020 |
| collection_details |
GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 |
| container_issue |
3 |
| title_short |
The influence of the coefficients of a system of wave equations coupled by velocities on its stabilization |
| url |
https://dx.doi.org/10.1007/s40324-020-00233-y |
| remote_bool |
true |
| author2 |
Ghader, Mouhammad Wehbe, Ali |
| author2Str |
Ghader, Mouhammad Wehbe, Ali |
| ppnlink |
815395299 |
| mediatype_str_mv |
c |
| isOA_txt |
false |
| hochschulschrift_bool |
false |
| doi_str |
10.1007/s40324-020-00233-y |
| up_date |
2024-07-04T02:15:26.309Z |
| _version_ |
1803612928146931712 |
| fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR044767587</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20220112030112.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">210807s2020 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s40324-020-00233-y</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR044767587</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s40324-020-00233-y-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">ASE</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Akil, Mohammad</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="4"><subfield code="a">The influence of the coefficients of a system of wave equations coupled by velocities on its stabilization</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2020</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Sociedad Española de Matemática Aplicada 2020</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract In this work, we consider a system of two wave equations coupled by velocities in a one-dimensional space, with one boundary fractional damping. First, we show that the system is strongly asymptotically stable if and only if the coupling parameter b of the two equations is outside a discrete set of exceptional real values. Next, we show that our system is not uniformly stable. Hence, we look for a polynomial decay rate for smooth initial data. Using a frequency domain approach combined with the multiplier method, we prove that the energy decay rate is greatly influenced by the nature of the coupling parameter b, the arithmetic property of the wave propagation speed a and the order of the fractional damping %$\alpha %$. Indeed, under the equal speed propagation condition, i.e., %$a=1%$, we establish an optimal polynomial energy decay rate of type %$t^{-\frac{2}{{1-\alpha }}}%$ if the coupling parameter %$b\notin \pi {\mathbb {Z}}%$ and of type %$t^{-\frac{2}{{5-\alpha }}}%$ if the coupling parameter %$b\in \pi {\mathbb {Z}}%$. Furthermore, when the wave propagates with different speeds, i.e., %$a\not =1%$, we prove that, for any rational number %$\sqrt{a}%$ and almost all irrational numbers %$\sqrt{a}%$, the energy of our system decays polynomially to zero like as %$t^{-\frac{2}{{5-\alpha }}}%$. This result still holds if %$a\in {\mathbb {Q}}%$, %$\sqrt{a}\notin {\mathbb {Q}}%$ and b small enough.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Coupled wave equations</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fractional boundary damping</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Strong stability</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Uniform stability</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Polynomial stability</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Ghader, Mouhammad</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Wehbe, Ali</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">SeMA journal</subfield><subfield code="d">Berlin : Springer, 2010</subfield><subfield code="g">78(2020), 3 vom: 02. Nov., Seite 287-333</subfield><subfield code="w">(DE-627)815395299</subfield><subfield code="w">(DE-600)2805493-3</subfield><subfield code="x">2254-3902</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:78</subfield><subfield code="g">year:2020</subfield><subfield code="g">number:3</subfield><subfield code="g">day:02</subfield><subfield code="g">month:11</subfield><subfield code="g">pages:287-333</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1007/s40324-020-00233-y</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_SPRINGER</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_11</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_20</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_22</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_23</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_24</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_31</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_32</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_39</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_40</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_60</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_62</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_63</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_65</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_69</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_73</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_74</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_90</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_95</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_100</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_105</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_110</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_120</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_138</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_150</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_151</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_152</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_161</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_170</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_171</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_187</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_213</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_224</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_230</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_250</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_281</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_285</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_293</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_370</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_602</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_636</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_702</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2001</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2003</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2004</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2005</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2006</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2007</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2008</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2009</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2010</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2011</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2014</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2015</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2018</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2020</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2021</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2025</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2026</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2027</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2031</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2034</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2037</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2038</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2039</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2044</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2048</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2049</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2050</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2055</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2056</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2057</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2059</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2061</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2064</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2065</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2068</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2088</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2093</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2106</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2107</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2108</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2110</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2111</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2112</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2113</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2118</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2122</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2129</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2143</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2144</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2147</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2148</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2152</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2153</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2188</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2190</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2232</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2336</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2446</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2470</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2472</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2507</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2522</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2548</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4035</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4037</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4046</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4112</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4125</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4126</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4242</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4246</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4249</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4251</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4305</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4306</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4307</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4313</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4322</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4323</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4324</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4325</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4326</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4328</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4333</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4334</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4335</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4336</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4338</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4393</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4700</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">78</subfield><subfield code="j">2020</subfield><subfield code="e">3</subfield><subfield code="b">02</subfield><subfield code="c">11</subfield><subfield code="h">287-333</subfield></datafield></record></collection>
|
| score |
7.4024944 |