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    Global existence and uniform stability of solutions for a quasilinear viscoelastic problem

    Global existence and uniform stability of solutions for a quasilinear viscoelastic problem. MATHEMATICAL METHODS IN THE APPLIED SCIENCES 30 (6).

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    Abstract

    Abstract In this paper the nonlinear viscoelastic wave equation in canonical form |ut|ρutt − ∆u − ∆utt + � t 0 g(t − τ)∆u(τ )dτ = b|u|p−2u with Dirichlet boundary condition is considered. By introducing a new functional and using the potential well method, we show that the damping induced by the viscoelastic term is enough to ensure global existence and uniformly decay of solutions provided that the initial data are in some stable set. Keywords and phrases: Global existence, Exponential decay, Nonlinear source, Relaxation function, Polynomial decay, Viscoelasticity.

    Item Type: Article
    Subjects: Math
    Department: College of Computing and Mathematics > Mathematics
    Depositing User: AbdulRahman
    Date Deposited: 19 Mar 2008 08:19
    Last Modified: 01 Nov 2019 13:24
    URI: http://eprints.kfupm.edu.sa/id/eprint/520