Exponential decay for solutions to semilinear damped wave equation

Handle URI:
http://hdl.handle.net/10754/561896
Title:
Exponential decay for solutions to semilinear damped wave equation
Authors:
Gerbi, Stéphane; Said-Houari, Belkacem
Abstract:
This paper is concerned with decay estimate of solutions to the semilinear wave equation with strong damping in a bounded domain. Intro- ducing an appropriate Lyapunov function, we prove that when the damping is linear, we can find initial data, for which the solution decays exponentially. This result improves an early one in [4].
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
American Institute of Mathematical Sciences
Journal:
Discrete and Continuous Dynamical Systems - Series S
Issue Date:
Oct-2011
DOI:
10.3934/dcdss.2012.5.559
Type:
Article
ISSN:
19371632
Sponsors:
The second author was supported by MIRA 2007 project of the Region Rhone-Alpes. This author wishes to thank Univ. de Savoie of Chambery for its kind hospitality. Moreover, the two authors wish to thank the referee for his useful remarks and his careful reading of the proofs presented in this paper.
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.accessioned2015-08-03T09:33:33Zen
dc.date.available2015-08-03T09:33:33Zen
dc.date.issued2011-10en
dc.identifier.issn19371632en
dc.identifier.doi10.3934/dcdss.2012.5.559en
dc.identifier.urihttp://hdl.handle.net/10754/561896en
dc.description.abstractThis paper is concerned with decay estimate of solutions to the semilinear wave equation with strong damping in a bounded domain. Intro- ducing an appropriate Lyapunov function, we prove that when the damping is linear, we can find initial data, for which the solution decays exponentially. This result improves an early one in [4].en
dc.description.sponsorshipThe second author was supported by MIRA 2007 project of the Region Rhone-Alpes. This author wishes to thank Univ. de Savoie of Chambery for its kind hospitality. Moreover, the two authors wish to thank the referee for his useful remarks and his careful reading of the proofs presented in this paper.en
dc.publisherAmerican Institute of Mathematical Sciencesen
dc.subjectDecay rateen
dc.subjectGlobal existenceen
dc.subjectPositive initial energyen
dc.subjectStable seten
dc.subjectStrong dampingen
dc.titleExponential decay for solutions to semilinear damped wave equationen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalDiscrete and Continuous Dynamical Systems - Series Sen
dc.contributor.institutionLaboratoire de Mathématiques, Université de Savoie, 3376 Le Bourget du Lac, Franceen
kaust.authorSaid-Houari, Belkacemen
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