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

Mokhtar Kirane, Belkacem Said-Houari

Research output: Contribution to journalArticlepeer-review

141 Scopus citations


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.
Original languageEnglish (US)
Pages (from-to)1065-1082
Number of pages18
JournalZeitschrift für angewandte Mathematik und Physik
Issue number6
StatePublished - Jul 7 2011

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01

ASJC Scopus subject areas

  • General Physics and Astronomy
  • Applied Mathematics
  • General Mathematics


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