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
Journal:
Nonlinear Analysis, Theory, Methods and 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.publisherElsevieren
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 and 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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