Stability of Wave Equations on Riemannian Manifolds with Locally Boundary Fractional Feedback Laws Under Geometric Conditions
Abstract In this paper, we consider a multidimensional wave equation with boundary fractional damping acting on part of the boundary on a Riemannian manifold. Firstly, using a general criterion of Arendt–Batty, we prove the strong stability of the system under feedback control of fractional order $$...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Ge, Hui [verfasserIn] |
|---|
| Format: |
Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
2022 |
|---|
| Schlagwörter: |
|---|
| Anmerkung: |
© Mathematica Josephina, Inc. 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
|---|
| Übergeordnetes Werk: |
Enthalten in: The journal of geometric analysis - Springer US, 1991, 33(2022), 2 vom: 19. Dez. |
|---|---|
| Übergeordnetes Werk: |
volume:33 ; year:2022 ; number:2 ; day:19 ; month:12 |
| Links: |
|---|
| DOI / URN: |
10.1007/s12220-022-01100-0 |
|---|
| Katalog-ID: |
OLC2080177931 |
|---|
| LEADER | 01000caa a22002652 4500 | ||
|---|---|---|---|
| 001 | OLC2080177931 | ||
| 003 | DE-627 | ||
| 005 | 20230506145533.0 | ||
| 007 | tu | ||
| 008 | 230131s2022 xx ||||| 00| ||eng c | ||
| 024 | 7 | |a 10.1007/s12220-022-01100-0 |2 doi | |
| 035 | |a (DE-627)OLC2080177931 | ||
| 035 | |a (DE-He213)s12220-022-01100-0-p | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rakwb | ||
| 041 | |a eng | ||
| 082 | 0 | 4 | |a 510 |q VZ |
| 084 | |a 17,1 |2 ssgn | ||
| 100 | 1 | |a Ge, Hui |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a Stability of Wave Equations on Riemannian Manifolds with Locally Boundary Fractional Feedback Laws Under Geometric Conditions |
| 264 | 1 | |c 2022 | |
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a ohne Hilfsmittel zu benutzen |b n |2 rdamedia | ||
| 338 | |a Band |b nc |2 rdacarrier | ||
| 500 | |a © Mathematica Josephina, Inc. 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. | ||
| 520 | |a Abstract In this paper, we consider a multidimensional wave equation with boundary fractional damping acting on part of the boundary on a Riemannian manifold. Firstly, using a general criterion of Arendt–Batty, we prove the strong stability of the system under feedback control of fractional order $$1<\alpha <2$$. Next, using the frequency domain approach combined with the multiplier method, we obtain a polynomial decay rate for the above system under some geometric assumptions on the domain. In addition, we give an example to illustrate the effectiveness of the boundary fractional feedback. | ||
| 650 | 4 | |a Strong stability | |
| 650 | 4 | |a Non-uniform stability | |
| 650 | 4 | |a Geometric condition | |
| 650 | 4 | |a Fractional feedback law | |
| 700 | 1 | |a Zhang, Zhifei |0 (orcid)0000-0002-1702-336X |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t The journal of geometric analysis |d Springer US, 1991 |g 33(2022), 2 vom: 19. Dez. |w (DE-627)131006398 |w (DE-600)1086949-9 |w (DE-576)028039211 |x 1050-6926 |7 nnns |
| 773 | 1 | 8 | |g volume:33 |g year:2022 |g number:2 |g day:19 |g month:12 |
| 856 | 4 | 1 | |u https://doi.org/10.1007/s12220-022-01100-0 |z lizenzpflichtig |3 Volltext |
| 912 | |a GBV_USEFLAG_A | ||
| 912 | |a SYSFLAG_A | ||
| 912 | |a GBV_OLC | ||
| 912 | |a SSG-OLC-MAT | ||
| 912 | |a SSG-OPC-MAT | ||
| 912 | |a GBV_ILN_2409 | ||
| 951 | |a AR | ||
| 952 | |d 33 |j 2022 |e 2 |b 19 |c 12 | ||
| author_variant |
h g hg z z zz |
|---|---|
| matchkey_str |
article:10506926:2022----::tbltowveutosnimninaiodwtlclyonayrcinleda |
| hierarchy_sort_str |
2022 |
| publishDate |
2022 |
| allfields |
10.1007/s12220-022-01100-0 doi (DE-627)OLC2080177931 (DE-He213)s12220-022-01100-0-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Ge, Hui verfasserin aut Stability of Wave Equations on Riemannian Manifolds with Locally Boundary Fractional Feedback Laws Under Geometric Conditions 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Mathematica Josephina, Inc. 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In this paper, we consider a multidimensional wave equation with boundary fractional damping acting on part of the boundary on a Riemannian manifold. Firstly, using a general criterion of Arendt–Batty, we prove the strong stability of the system under feedback control of fractional order $$1<\alpha <2$$. Next, using the frequency domain approach combined with the multiplier method, we obtain a polynomial decay rate for the above system under some geometric assumptions on the domain. In addition, we give an example to illustrate the effectiveness of the boundary fractional feedback. Strong stability Non-uniform stability Geometric condition Fractional feedback law Zhang, Zhifei (orcid)0000-0002-1702-336X aut Enthalten in The journal of geometric analysis Springer US, 1991 33(2022), 2 vom: 19. Dez. (DE-627)131006398 (DE-600)1086949-9 (DE-576)028039211 1050-6926 nnns volume:33 year:2022 number:2 day:19 month:12 https://doi.org/10.1007/s12220-022-01100-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2409 AR 33 2022 2 19 12 |
| spelling |
10.1007/s12220-022-01100-0 doi (DE-627)OLC2080177931 (DE-He213)s12220-022-01100-0-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Ge, Hui verfasserin aut Stability of Wave Equations on Riemannian Manifolds with Locally Boundary Fractional Feedback Laws Under Geometric Conditions 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Mathematica Josephina, Inc. 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In this paper, we consider a multidimensional wave equation with boundary fractional damping acting on part of the boundary on a Riemannian manifold. Firstly, using a general criterion of Arendt–Batty, we prove the strong stability of the system under feedback control of fractional order $$1<\alpha <2$$. Next, using the frequency domain approach combined with the multiplier method, we obtain a polynomial decay rate for the above system under some geometric assumptions on the domain. In addition, we give an example to illustrate the effectiveness of the boundary fractional feedback. Strong stability Non-uniform stability Geometric condition Fractional feedback law Zhang, Zhifei (orcid)0000-0002-1702-336X aut Enthalten in The journal of geometric analysis Springer US, 1991 33(2022), 2 vom: 19. Dez. (DE-627)131006398 (DE-600)1086949-9 (DE-576)028039211 1050-6926 nnns volume:33 year:2022 number:2 day:19 month:12 https://doi.org/10.1007/s12220-022-01100-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2409 AR 33 2022 2 19 12 |
| allfields_unstemmed |
10.1007/s12220-022-01100-0 doi (DE-627)OLC2080177931 (DE-He213)s12220-022-01100-0-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Ge, Hui verfasserin aut Stability of Wave Equations on Riemannian Manifolds with Locally Boundary Fractional Feedback Laws Under Geometric Conditions 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Mathematica Josephina, Inc. 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In this paper, we consider a multidimensional wave equation with boundary fractional damping acting on part of the boundary on a Riemannian manifold. Firstly, using a general criterion of Arendt–Batty, we prove the strong stability of the system under feedback control of fractional order $$1<\alpha <2$$. Next, using the frequency domain approach combined with the multiplier method, we obtain a polynomial decay rate for the above system under some geometric assumptions on the domain. In addition, we give an example to illustrate the effectiveness of the boundary fractional feedback. Strong stability Non-uniform stability Geometric condition Fractional feedback law Zhang, Zhifei (orcid)0000-0002-1702-336X aut Enthalten in The journal of geometric analysis Springer US, 1991 33(2022), 2 vom: 19. Dez. (DE-627)131006398 (DE-600)1086949-9 (DE-576)028039211 1050-6926 nnns volume:33 year:2022 number:2 day:19 month:12 https://doi.org/10.1007/s12220-022-01100-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2409 AR 33 2022 2 19 12 |
| allfieldsGer |
10.1007/s12220-022-01100-0 doi (DE-627)OLC2080177931 (DE-He213)s12220-022-01100-0-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Ge, Hui verfasserin aut Stability of Wave Equations on Riemannian Manifolds with Locally Boundary Fractional Feedback Laws Under Geometric Conditions 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Mathematica Josephina, Inc. 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In this paper, we consider a multidimensional wave equation with boundary fractional damping acting on part of the boundary on a Riemannian manifold. Firstly, using a general criterion of Arendt–Batty, we prove the strong stability of the system under feedback control of fractional order $$1<\alpha <2$$. Next, using the frequency domain approach combined with the multiplier method, we obtain a polynomial decay rate for the above system under some geometric assumptions on the domain. In addition, we give an example to illustrate the effectiveness of the boundary fractional feedback. Strong stability Non-uniform stability Geometric condition Fractional feedback law Zhang, Zhifei (orcid)0000-0002-1702-336X aut Enthalten in The journal of geometric analysis Springer US, 1991 33(2022), 2 vom: 19. Dez. (DE-627)131006398 (DE-600)1086949-9 (DE-576)028039211 1050-6926 nnns volume:33 year:2022 number:2 day:19 month:12 https://doi.org/10.1007/s12220-022-01100-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2409 AR 33 2022 2 19 12 |
| allfieldsSound |
10.1007/s12220-022-01100-0 doi (DE-627)OLC2080177931 (DE-He213)s12220-022-01100-0-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Ge, Hui verfasserin aut Stability of Wave Equations on Riemannian Manifolds with Locally Boundary Fractional Feedback Laws Under Geometric Conditions 2022 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Mathematica Josephina, Inc. 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In this paper, we consider a multidimensional wave equation with boundary fractional damping acting on part of the boundary on a Riemannian manifold. Firstly, using a general criterion of Arendt–Batty, we prove the strong stability of the system under feedback control of fractional order $$1<\alpha <2$$. Next, using the frequency domain approach combined with the multiplier method, we obtain a polynomial decay rate for the above system under some geometric assumptions on the domain. In addition, we give an example to illustrate the effectiveness of the boundary fractional feedback. Strong stability Non-uniform stability Geometric condition Fractional feedback law Zhang, Zhifei (orcid)0000-0002-1702-336X aut Enthalten in The journal of geometric analysis Springer US, 1991 33(2022), 2 vom: 19. Dez. (DE-627)131006398 (DE-600)1086949-9 (DE-576)028039211 1050-6926 nnns volume:33 year:2022 number:2 day:19 month:12 https://doi.org/10.1007/s12220-022-01100-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2409 AR 33 2022 2 19 12 |
| language |
English |
| source |
Enthalten in The journal of geometric analysis 33(2022), 2 vom: 19. Dez. volume:33 year:2022 number:2 day:19 month:12 |
| sourceStr |
Enthalten in The journal of geometric analysis 33(2022), 2 vom: 19. Dez. volume:33 year:2022 number:2 day:19 month:12 |
| format_phy_str_mv |
Article |
| institution |
findex.gbv.de |
| topic_facet |
Strong stability Non-uniform stability Geometric condition Fractional feedback law |
| dewey-raw |
510 |
| isfreeaccess_bool |
false |
| container_title |
The journal of geometric analysis |
| authorswithroles_txt_mv |
Ge, Hui @@aut@@ Zhang, Zhifei @@aut@@ |
| publishDateDaySort_date |
2022-12-19T00:00:00Z |
| hierarchy_top_id |
131006398 |
| dewey-sort |
3510 |
| id |
OLC2080177931 |
| 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">OLC2080177931</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230506145533.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">230131s2022 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s12220-022-01100-0</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2080177931</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s12220-022-01100-0-p</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">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Ge, Hui</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Stability of Wave Equations on Riemannian Manifolds with Locally Boundary Fractional Feedback Laws Under Geometric Conditions</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2022</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">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Mathematica Josephina, Inc. 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract In this paper, we consider a multidimensional wave equation with boundary fractional damping acting on part of the boundary on a Riemannian manifold. Firstly, using a general criterion of Arendt–Batty, we prove the strong stability of the system under feedback control of fractional order $$1<\alpha <2$$. Next, using the frequency domain approach combined with the multiplier method, we obtain a polynomial decay rate for the above system under some geometric assumptions on the domain. In addition, we give an example to illustrate the effectiveness of the boundary fractional feedback.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Strong stability</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Non-uniform stability</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Geometric condition</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fractional feedback law</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Zhang, Zhifei</subfield><subfield code="0">(orcid)0000-0002-1702-336X</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">The journal of geometric analysis</subfield><subfield code="d">Springer US, 1991</subfield><subfield code="g">33(2022), 2 vom: 19. Dez.</subfield><subfield code="w">(DE-627)131006398</subfield><subfield code="w">(DE-600)1086949-9</subfield><subfield code="w">(DE-576)028039211</subfield><subfield code="x">1050-6926</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:33</subfield><subfield code="g">year:2022</subfield><subfield code="g">number:2</subfield><subfield code="g">day:19</subfield><subfield code="g">month:12</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/s12220-022-01100-0</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_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2409</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">33</subfield><subfield code="j">2022</subfield><subfield code="e">2</subfield><subfield code="b">19</subfield><subfield code="c">12</subfield></datafield></record></collection>
|
| author |
Ge, Hui |
| spellingShingle |
Ge, Hui ddc 510 ssgn 17,1 misc Strong stability misc Non-uniform stability misc Geometric condition misc Fractional feedback law Stability of Wave Equations on Riemannian Manifolds with Locally Boundary Fractional Feedback Laws Under Geometric Conditions |
| authorStr |
Ge, Hui |
| ppnlink_with_tag_str_mv |
@@773@@(DE-627)131006398 |
| format |
Article |
| dewey-ones |
510 - Mathematics |
| delete_txt_mv |
keep |
| author_role |
aut aut |
| collection |
OLC |
| remote_str |
false |
| illustrated |
Not Illustrated |
| issn |
1050-6926 |
| topic_title |
510 VZ 17,1 ssgn Stability of Wave Equations on Riemannian Manifolds with Locally Boundary Fractional Feedback Laws Under Geometric Conditions Strong stability Non-uniform stability Geometric condition Fractional feedback law |
| topic |
ddc 510 ssgn 17,1 misc Strong stability misc Non-uniform stability misc Geometric condition misc Fractional feedback law |
| topic_unstemmed |
ddc 510 ssgn 17,1 misc Strong stability misc Non-uniform stability misc Geometric condition misc Fractional feedback law |
| topic_browse |
ddc 510 ssgn 17,1 misc Strong stability misc Non-uniform stability misc Geometric condition misc Fractional feedback law |
| format_facet |
Aufsätze Gedruckte Aufsätze |
| format_main_str_mv |
Text Zeitschrift/Artikel |
| carriertype_str_mv |
nc |
| hierarchy_parent_title |
The journal of geometric analysis |
| hierarchy_parent_id |
131006398 |
| dewey-tens |
510 - Mathematics |
| hierarchy_top_title |
The journal of geometric analysis |
| isfreeaccess_txt |
false |
| familylinks_str_mv |
(DE-627)131006398 (DE-600)1086949-9 (DE-576)028039211 |
| title |
Stability of Wave Equations on Riemannian Manifolds with Locally Boundary Fractional Feedback Laws Under Geometric Conditions |
| ctrlnum |
(DE-627)OLC2080177931 (DE-He213)s12220-022-01100-0-p |
| title_full |
Stability of Wave Equations on Riemannian Manifolds with Locally Boundary Fractional Feedback Laws Under Geometric Conditions |
| author_sort |
Ge, Hui |
| journal |
The journal of geometric analysis |
| journalStr |
The journal of geometric analysis |
| lang_code |
eng |
| isOA_bool |
false |
| dewey-hundreds |
500 - Science |
| recordtype |
marc |
| publishDateSort |
2022 |
| contenttype_str_mv |
txt |
| author_browse |
Ge, Hui Zhang, Zhifei |
| container_volume |
33 |
| class |
510 VZ 17,1 ssgn |
| format_se |
Aufsätze |
| author-letter |
Ge, Hui |
| doi_str_mv |
10.1007/s12220-022-01100-0 |
| normlink |
(ORCID)0000-0002-1702-336X |
| normlink_prefix_str_mv |
(orcid)0000-0002-1702-336X |
| dewey-full |
510 |
| title_sort |
stability of wave equations on riemannian manifolds with locally boundary fractional feedback laws under geometric conditions |
| title_auth |
Stability of Wave Equations on Riemannian Manifolds with Locally Boundary Fractional Feedback Laws Under Geometric Conditions |
| abstract |
Abstract In this paper, we consider a multidimensional wave equation with boundary fractional damping acting on part of the boundary on a Riemannian manifold. Firstly, using a general criterion of Arendt–Batty, we prove the strong stability of the system under feedback control of fractional order $$1<\alpha <2$$. Next, using the frequency domain approach combined with the multiplier method, we obtain a polynomial decay rate for the above system under some geometric assumptions on the domain. In addition, we give an example to illustrate the effectiveness of the boundary fractional feedback. © Mathematica Josephina, Inc. 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| abstractGer |
Abstract In this paper, we consider a multidimensional wave equation with boundary fractional damping acting on part of the boundary on a Riemannian manifold. Firstly, using a general criterion of Arendt–Batty, we prove the strong stability of the system under feedback control of fractional order $$1<\alpha <2$$. Next, using the frequency domain approach combined with the multiplier method, we obtain a polynomial decay rate for the above system under some geometric assumptions on the domain. In addition, we give an example to illustrate the effectiveness of the boundary fractional feedback. © Mathematica Josephina, Inc. 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| abstract_unstemmed |
Abstract In this paper, we consider a multidimensional wave equation with boundary fractional damping acting on part of the boundary on a Riemannian manifold. Firstly, using a general criterion of Arendt–Batty, we prove the strong stability of the system under feedback control of fractional order $$1<\alpha <2$$. Next, using the frequency domain approach combined with the multiplier method, we obtain a polynomial decay rate for the above system under some geometric assumptions on the domain. In addition, we give an example to illustrate the effectiveness of the boundary fractional feedback. © Mathematica Josephina, Inc. 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| collection_details |
GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_2409 |
| container_issue |
2 |
| title_short |
Stability of Wave Equations on Riemannian Manifolds with Locally Boundary Fractional Feedback Laws Under Geometric Conditions |
| url |
https://doi.org/10.1007/s12220-022-01100-0 |
| remote_bool |
false |
| author2 |
Zhang, Zhifei |
| author2Str |
Zhang, Zhifei |
| ppnlink |
131006398 |
| mediatype_str_mv |
n |
| isOA_txt |
false |
| hochschulschrift_bool |
false |
| doi_str |
10.1007/s12220-022-01100-0 |
| up_date |
2024-07-04T03:08:10.849Z |
| _version_ |
1803616246419161088 |
| 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">OLC2080177931</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230506145533.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">230131s2022 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s12220-022-01100-0</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2080177931</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s12220-022-01100-0-p</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">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Ge, Hui</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Stability of Wave Equations on Riemannian Manifolds with Locally Boundary Fractional Feedback Laws Under Geometric Conditions</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2022</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">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Mathematica Josephina, Inc. 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract In this paper, we consider a multidimensional wave equation with boundary fractional damping acting on part of the boundary on a Riemannian manifold. Firstly, using a general criterion of Arendt–Batty, we prove the strong stability of the system under feedback control of fractional order $$1<\alpha <2$$. Next, using the frequency domain approach combined with the multiplier method, we obtain a polynomial decay rate for the above system under some geometric assumptions on the domain. In addition, we give an example to illustrate the effectiveness of the boundary fractional feedback.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Strong stability</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Non-uniform stability</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Geometric condition</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fractional feedback law</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Zhang, Zhifei</subfield><subfield code="0">(orcid)0000-0002-1702-336X</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">The journal of geometric analysis</subfield><subfield code="d">Springer US, 1991</subfield><subfield code="g">33(2022), 2 vom: 19. Dez.</subfield><subfield code="w">(DE-627)131006398</subfield><subfield code="w">(DE-600)1086949-9</subfield><subfield code="w">(DE-576)028039211</subfield><subfield code="x">1050-6926</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:33</subfield><subfield code="g">year:2022</subfield><subfield code="g">number:2</subfield><subfield code="g">day:19</subfield><subfield code="g">month:12</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/s12220-022-01100-0</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_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2409</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">33</subfield><subfield code="j">2022</subfield><subfield code="e">2</subfield><subfield code="b">19</subfield><subfield code="c">12</subfield></datafield></record></collection>
|
| score |
7.4023743 |