Existence and asymptotic stability of a viscoelastic wave equation with a delay

Handle URI:
http://hdl.handle.net/10754/561815
Title:
Existence and asymptotic stability of a viscoelastic wave equation with a delay
Authors:
Kirane, Mokhtar; Said-Houari, Belkacem
Abstract:
In this paper, we consider the viscoelastic wave equation with a delay term in internal feedbacks; namely, we investigate the following problem, together with initial conditions and boundary conditions of Dirichlet type. Here (x, t) ∈ Ω × (0, ∞), g is a positive real valued decreasing function and μ1, μ2 are positive constants. Under an hypothesis between the weight of the delay term in the feedback and the weight of the term without delay, using the Faedo-Galerkin approximations together with some energy estimates, we prove the global existence of the solutions. Under the same assumptions, general decay results of the energy are established via suitable Lyapunov functionals. © 2011 Springer Basel AG.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
Springer Verlag
Journal:
Zeitschrift fur Angewandte Mathematik und Physik
Issue Date:
7-Jul-2011
DOI:
10.1007/s00033-011-0145-0
Type:
Article
ISSN:
00442275
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorKirane, Mokhtaren
dc.contributor.authorSaid-Houari, Belkacemen
dc.date.accessioned2015-08-03T09:31:33Zen
dc.date.available2015-08-03T09:31:33Zen
dc.date.issued2011-07-07en
dc.identifier.issn00442275en
dc.identifier.doi10.1007/s00033-011-0145-0en
dc.identifier.urihttp://hdl.handle.net/10754/561815en
dc.description.abstractIn this paper, we consider the viscoelastic wave equation with a delay term in internal feedbacks; namely, we investigate the following problem, together with initial conditions and boundary conditions of Dirichlet type. Here (x, t) ∈ Ω × (0, ∞), g is a positive real valued decreasing function and μ1, μ2 are positive constants. Under an hypothesis between the weight of the delay term in the feedback and the weight of the term without delay, using the Faedo-Galerkin approximations together with some energy estimates, we prove the global existence of the solutions. Under the same assumptions, general decay results of the energy are established via suitable Lyapunov functionals. © 2011 Springer Basel AG.en
dc.publisherSpringer Verlagen
dc.subjectDelay feedbacksen
dc.subjectGeneral decayen
dc.subjectGlobal existenceen
dc.subjectRelaxation functionen
dc.titleExistence and asymptotic stability of a viscoelastic wave equation with a delayen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalZeitschrift fur Angewandte Mathematik und Physiken
dc.contributor.institutionMathématiques, Image et Applications Pole Sciences et Technologie, Université de la Rochelle, La Rochelle, Franceen
dc.contributor.institutionDepartment of Mathematics and Statistics, University of Konstanz, 78457 Konstanz, Germanyen
kaust.authorSaid-Houari, Belkacemen
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