Global existence and exponential growth for a viscoelastic wave equation with dynamic boundary conditions

Handle URI:
http://hdl.handle.net/10754/575570
Title:
Global existence and exponential growth for a viscoelastic wave equation with dynamic boundary conditions
Authors:
Gerbi, Stéphane; Said-Houari, Belkacem
Abstract:
The goal of this work is to study a model of the wave equation with dynamic boundary conditions and a viscoelastic term. First, applying the Faedo-Galerkin method combined with the fixed point theorem, we show the existence and uniqueness of a local in time solution. Second, we show that under some restrictions on the initial data, the solution continues to exist globally in time. On the other hand, if the interior source dominates the boundary damping, then the solution is unbounded and grows as an exponential function. In addition, in the absence of the strong damping, then the solution ceases to exist and blows up in finite time.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
Walter de Gruyter GmbH
Journal:
Advances in Nonlinear Analysis
Issue Date:
15-Jan-2013
DOI:
10.1515/anona-2012-0027
Type:
Article
ISSN:
2191-9496; 2191-950X
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.accessioned2015-08-24T08:33:07Zen
dc.date.available2015-08-24T08:33:07Zen
dc.date.issued2013-01-15en
dc.identifier.issn2191-9496en
dc.identifier.issn2191-950Xen
dc.identifier.doi10.1515/anona-2012-0027en
dc.identifier.urihttp://hdl.handle.net/10754/575570en
dc.description.abstractThe goal of this work is to study a model of the wave equation with dynamic boundary conditions and a viscoelastic term. First, applying the Faedo-Galerkin method combined with the fixed point theorem, we show the existence and uniqueness of a local in time solution. Second, we show that under some restrictions on the initial data, the solution continues to exist globally in time. On the other hand, if the interior source dominates the boundary damping, then the solution is unbounded and grows as an exponential function. In addition, in the absence of the strong damping, then the solution ceases to exist and blows up in finite time.en
dc.publisherWalter de Gruyter GmbHen
dc.titleGlobal existence and exponential growth for a viscoelastic wave equation with dynamic boundary conditionsen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalAdvances in Nonlinear Analysisen
dc.contributor.institutionUniv Savoie, Math Lab, F-73376 Le Bourget Du Lac, Franceen
dc.contributor.institutionCNRS, UMR 5128, F-73376 Le Bourget Du Lac, Franceen
kaust.authorSaid-Houari, Belkacemen
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.