Stochastic Allen–Cahn equation with mobility
Abstract We introduce a class of stochastic Allen–Cahn equations with a mobility coefficient and colored noise. For initial data with finite free energy, we analyze the corresponding Cauchy problem on the d-dimensional torus in the time interval [0, T]. Assuming that %$d\le 3%$ and that the potentia...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Bertini, Lorenzo [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2017 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer International Publishing AG 2017 |
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| Übergeordnetes Werk: |
Enthalten in: Nonlinear differential equations and applications - [Cham (ZG)] : [Springer International Publishing AG], 1994, 24(2017), 5 vom: 14. Aug. |
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| Übergeordnetes Werk: |
volume:24 ; year:2017 ; number:5 ; day:14 ; month:08 |
| Links: |
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| DOI / URN: |
10.1007/s00030-017-0477-3 |
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| Katalog-ID: |
SPR000317284 |
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| 245 | 1 | 0 | |a Stochastic Allen–Cahn equation with mobility |
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| 520 | |a Abstract We introduce a class of stochastic Allen–Cahn equations with a mobility coefficient and colored noise. For initial data with finite free energy, we analyze the corresponding Cauchy problem on the d-dimensional torus in the time interval [0, T]. Assuming that %$d\le 3%$ and that the potential has quartic growth, we prove existence and uniqueness of the solution as a process u in %$L^2%$ with continuous paths, satisfying almost surely the regularity properties %$u\in C([0,T]; H^1)%$ and %$u\in L^2([0,T];H^2)%$. | ||
| 650 | 4 | |a Stochastic PDEs |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Allen–Cahn equation |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Well-posedness |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Buttà, Paolo |4 aut | |
| 700 | 1 | |a Pisante, Adriano |4 aut | |
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10.1007/s00030-017-0477-3 doi (DE-627)SPR000317284 (SPR)s00030-017-0477-3-e DE-627 ger DE-627 rakwb eng Bertini, Lorenzo verfasserin aut Stochastic Allen–Cahn equation with mobility 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer International Publishing AG 2017 Abstract We introduce a class of stochastic Allen–Cahn equations with a mobility coefficient and colored noise. For initial data with finite free energy, we analyze the corresponding Cauchy problem on the d-dimensional torus in the time interval [0, T]. Assuming that %$d\le 3%$ and that the potential has quartic growth, we prove existence and uniqueness of the solution as a process u in %$L^2%$ with continuous paths, satisfying almost surely the regularity properties %$u\in C([0,T]; H^1)%$ and %$u\in L^2([0,T];H^2)%$. Stochastic PDEs (dpeaa)DE-He213 Allen–Cahn equation (dpeaa)DE-He213 Well-posedness (dpeaa)DE-He213 Buttà, Paolo aut Pisante, Adriano aut Enthalten in Nonlinear differential equations and applications [Cham (ZG)] : [Springer International Publishing AG], 1994 24(2017), 5 vom: 14. Aug. (DE-627)271596031 (DE-600)1480580-7 1420-9004 nnns volume:24 year:2017 number:5 day:14 month:08 https://dx.doi.org/10.1007/s00030-017-0477-3 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_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_267 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_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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_4012 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_4277 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 24 2017 5 14 08 |
| spelling |
10.1007/s00030-017-0477-3 doi (DE-627)SPR000317284 (SPR)s00030-017-0477-3-e DE-627 ger DE-627 rakwb eng Bertini, Lorenzo verfasserin aut Stochastic Allen–Cahn equation with mobility 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer International Publishing AG 2017 Abstract We introduce a class of stochastic Allen–Cahn equations with a mobility coefficient and colored noise. For initial data with finite free energy, we analyze the corresponding Cauchy problem on the d-dimensional torus in the time interval [0, T]. Assuming that %$d\le 3%$ and that the potential has quartic growth, we prove existence and uniqueness of the solution as a process u in %$L^2%$ with continuous paths, satisfying almost surely the regularity properties %$u\in C([0,T]; H^1)%$ and %$u\in L^2([0,T];H^2)%$. Stochastic PDEs (dpeaa)DE-He213 Allen–Cahn equation (dpeaa)DE-He213 Well-posedness (dpeaa)DE-He213 Buttà, Paolo aut Pisante, Adriano aut Enthalten in Nonlinear differential equations and applications [Cham (ZG)] : [Springer International Publishing AG], 1994 24(2017), 5 vom: 14. Aug. (DE-627)271596031 (DE-600)1480580-7 1420-9004 nnns volume:24 year:2017 number:5 day:14 month:08 https://dx.doi.org/10.1007/s00030-017-0477-3 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_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_267 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_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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_4012 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_4277 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 24 2017 5 14 08 |
| allfields_unstemmed |
10.1007/s00030-017-0477-3 doi (DE-627)SPR000317284 (SPR)s00030-017-0477-3-e DE-627 ger DE-627 rakwb eng Bertini, Lorenzo verfasserin aut Stochastic Allen–Cahn equation with mobility 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer International Publishing AG 2017 Abstract We introduce a class of stochastic Allen–Cahn equations with a mobility coefficient and colored noise. For initial data with finite free energy, we analyze the corresponding Cauchy problem on the d-dimensional torus in the time interval [0, T]. Assuming that %$d\le 3%$ and that the potential has quartic growth, we prove existence and uniqueness of the solution as a process u in %$L^2%$ with continuous paths, satisfying almost surely the regularity properties %$u\in C([0,T]; H^1)%$ and %$u\in L^2([0,T];H^2)%$. Stochastic PDEs (dpeaa)DE-He213 Allen–Cahn equation (dpeaa)DE-He213 Well-posedness (dpeaa)DE-He213 Buttà, Paolo aut Pisante, Adriano aut Enthalten in Nonlinear differential equations and applications [Cham (ZG)] : [Springer International Publishing AG], 1994 24(2017), 5 vom: 14. Aug. (DE-627)271596031 (DE-600)1480580-7 1420-9004 nnns volume:24 year:2017 number:5 day:14 month:08 https://dx.doi.org/10.1007/s00030-017-0477-3 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_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_267 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_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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_4012 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_4277 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 24 2017 5 14 08 |
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10.1007/s00030-017-0477-3 doi (DE-627)SPR000317284 (SPR)s00030-017-0477-3-e DE-627 ger DE-627 rakwb eng Bertini, Lorenzo verfasserin aut Stochastic Allen–Cahn equation with mobility 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer International Publishing AG 2017 Abstract We introduce a class of stochastic Allen–Cahn equations with a mobility coefficient and colored noise. For initial data with finite free energy, we analyze the corresponding Cauchy problem on the d-dimensional torus in the time interval [0, T]. Assuming that %$d\le 3%$ and that the potential has quartic growth, we prove existence and uniqueness of the solution as a process u in %$L^2%$ with continuous paths, satisfying almost surely the regularity properties %$u\in C([0,T]; H^1)%$ and %$u\in L^2([0,T];H^2)%$. Stochastic PDEs (dpeaa)DE-He213 Allen–Cahn equation (dpeaa)DE-He213 Well-posedness (dpeaa)DE-He213 Buttà, Paolo aut Pisante, Adriano aut Enthalten in Nonlinear differential equations and applications [Cham (ZG)] : [Springer International Publishing AG], 1994 24(2017), 5 vom: 14. Aug. (DE-627)271596031 (DE-600)1480580-7 1420-9004 nnns volume:24 year:2017 number:5 day:14 month:08 https://dx.doi.org/10.1007/s00030-017-0477-3 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_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_267 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_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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_4012 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_4277 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 24 2017 5 14 08 |
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10.1007/s00030-017-0477-3 doi (DE-627)SPR000317284 (SPR)s00030-017-0477-3-e DE-627 ger DE-627 rakwb eng Bertini, Lorenzo verfasserin aut Stochastic Allen–Cahn equation with mobility 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer International Publishing AG 2017 Abstract We introduce a class of stochastic Allen–Cahn equations with a mobility coefficient and colored noise. For initial data with finite free energy, we analyze the corresponding Cauchy problem on the d-dimensional torus in the time interval [0, T]. Assuming that %$d\le 3%$ and that the potential has quartic growth, we prove existence and uniqueness of the solution as a process u in %$L^2%$ with continuous paths, satisfying almost surely the regularity properties %$u\in C([0,T]; H^1)%$ and %$u\in L^2([0,T];H^2)%$. Stochastic PDEs (dpeaa)DE-He213 Allen–Cahn equation (dpeaa)DE-He213 Well-posedness (dpeaa)DE-He213 Buttà, Paolo aut Pisante, Adriano aut Enthalten in Nonlinear differential equations and applications [Cham (ZG)] : [Springer International Publishing AG], 1994 24(2017), 5 vom: 14. Aug. (DE-627)271596031 (DE-600)1480580-7 1420-9004 nnns volume:24 year:2017 number:5 day:14 month:08 https://dx.doi.org/10.1007/s00030-017-0477-3 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_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_267 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_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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_4012 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_4277 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 24 2017 5 14 08 |
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English |
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Enthalten in Nonlinear differential equations and applications 24(2017), 5 vom: 14. Aug. volume:24 year:2017 number:5 day:14 month:08 |
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Enthalten in Nonlinear differential equations and applications 24(2017), 5 vom: 14. Aug. volume:24 year:2017 number:5 day:14 month:08 |
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Stochastic PDEs Allen–Cahn equation Well-posedness |
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Nonlinear differential equations and applications |
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Bertini, Lorenzo @@aut@@ Buttà, Paolo @@aut@@ Pisante, Adriano @@aut@@ |
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2017-08-14T00:00:00Z |
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stochastic allen–cahn equation with mobility |
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Stochastic Allen–Cahn equation with mobility |
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Abstract We introduce a class of stochastic Allen–Cahn equations with a mobility coefficient and colored noise. For initial data with finite free energy, we analyze the corresponding Cauchy problem on the d-dimensional torus in the time interval [0, T]. Assuming that %$d\le 3%$ and that the potential has quartic growth, we prove existence and uniqueness of the solution as a process u in %$L^2%$ with continuous paths, satisfying almost surely the regularity properties %$u\in C([0,T]; H^1)%$ and %$u\in L^2([0,T];H^2)%$. © Springer International Publishing AG 2017 |
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Abstract We introduce a class of stochastic Allen–Cahn equations with a mobility coefficient and colored noise. For initial data with finite free energy, we analyze the corresponding Cauchy problem on the d-dimensional torus in the time interval [0, T]. Assuming that %$d\le 3%$ and that the potential has quartic growth, we prove existence and uniqueness of the solution as a process u in %$L^2%$ with continuous paths, satisfying almost surely the regularity properties %$u\in C([0,T]; H^1)%$ and %$u\in L^2([0,T];H^2)%$. © Springer International Publishing AG 2017 |
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Abstract We introduce a class of stochastic Allen–Cahn equations with a mobility coefficient and colored noise. For initial data with finite free energy, we analyze the corresponding Cauchy problem on the d-dimensional torus in the time interval [0, T]. Assuming that %$d\le 3%$ and that the potential has quartic growth, we prove existence and uniqueness of the solution as a process u in %$L^2%$ with continuous paths, satisfying almost surely the regularity properties %$u\in C([0,T]; H^1)%$ and %$u\in L^2([0,T];H^2)%$. © Springer International Publishing AG 2017 |
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