Asymptotic stability and blow up for a semilinear damped wave equation with dynamic boundary conditions

Handle URI:
http://hdl.handle.net/10754/561936
Title:
Asymptotic stability and blow up for a semilinear damped wave equation with dynamic boundary conditions
Authors:
Gerbi, Stéphane; Said-Houari, Belkacem
Abstract:
In this paper we consider a multi-dimensional wave equation with dynamic boundary conditions, related to the KelvinVoigt damping. Global existence and asymptotic stability of solutions starting in a stable set are proved. Blow up for solutions of the problem with linear dynamic boundary conditions with initial data in the unstable set is also obtained. © 2011 Elsevier Ltd. All rights reserved.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
Elsevier BV
Journal:
Nonlinear Analysis: Theory, Methods & Applications
Issue Date:
Dec-2011
DOI:
10.1016/j.na.2011.07.026
ARXIV:
arXiv:0811.2783
Type:
Article
ISSN:
0362546X
Additional Links:
http://arxiv.org/abs/arXiv:0811.2783v3
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorGerbi, Stéphaneen
dc.contributor.authorSaid-Houari, Belkacemen
dc.date.accessioned2015-08-03T09:34:30Zen
dc.date.available2015-08-03T09:34:30Zen
dc.date.issued2011-12en
dc.identifier.issn0362546Xen
dc.identifier.doi10.1016/j.na.2011.07.026en
dc.identifier.urihttp://hdl.handle.net/10754/561936en
dc.description.abstractIn this paper we consider a multi-dimensional wave equation with dynamic boundary conditions, related to the KelvinVoigt damping. Global existence and asymptotic stability of solutions starting in a stable set are proved. Blow up for solutions of the problem with linear dynamic boundary conditions with initial data in the unstable set is also obtained. © 2011 Elsevier Ltd. All rights reserved.en
dc.publisherElsevier BVen
dc.relation.urlhttp://arxiv.org/abs/arXiv:0811.2783v3en
dc.subjectBlow upen
dc.subjectDamped wave equationsen
dc.subjectDynamic boundary conditionsen
dc.subjectGlobal solutionsen
dc.subjectKelvinVoigt dampingen
dc.subjectStable and unstable seten
dc.titleAsymptotic stability and blow up for a semilinear damped wave equation with dynamic boundary conditionsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalNonlinear Analysis: Theory, Methods & Applicationsen
dc.contributor.institutionUniversité de Savoie, LAMA, 73376 Le Bourget-du-Lac Cedex, Franceen
dc.identifier.arxividarXiv:0811.2783en
kaust.authorSaid-Houari, Belkacemen
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