Abstract
In this paper we consider a quasilinear viscoelastic wave equation with initial-boundary conditions, strong damping and source term. Under suitable assumptions on the initial data and the relaxation function, we establish a blow-up result of a solution for negative initial energy and some positive initial energy if the influence of the source term is greater than the dissipation. We show that the solution exists globally for any initial data if the influence of dissipation is greater than the source term.
Highlights
Berrimi and Messaoudi [ ] considered the following initial-boundary value problem:
1 Introduction In this work, we study the following quasilinear viscoelastic wave equation with initialboundary value conditions, strong damping and source term:
In, where is a bounded domain of Rn (n ≥ ) with smooth boundary ∂, and ρ, b >, p > are constants. He obtained a general decay of the solution for certain class of relaxation functions and initial data in the stable set, and showed that the solution blows up in a larger class of initial positive energy
Summary
Berrimi and Messaoudi [ ] considered the following initial-boundary value problem: Where is a bounded domain of Rn (n ≥ ) with smooth boundary ∂ , γ is a positive constant, and g is a nonnegative and decreasing function. They obtained a local existence result and proved, for certain initial data and suitable conditions on g and γ
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