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