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

Mokhtar Kirane, Belkacem Said-Houari

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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.

Original languageBritish English
Pages (from-to)1065-1082
Number of pages18
JournalZeitschrift fur Angewandte Mathematik und Physik
Issue number6
StatePublished - Dec 2011


  • Delay feedbacks
  • General decay
  • Global existence
  • Relaxation function


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