Abstract
In this paper, we consider a quasilinear viscoelastic wave equation with acoustic boundary conditions. Under some appropriate assumption on the relaxation function g, the function Φ, p > max { rho +2, m, q,2}, and the initial data, we prove a global nonexistence of solutions for a quasilinear viscoelastic wave equation with positive initial energy.
Highlights
System (1)–(6) is a model of a quasilinear viscoelastic wave equation with acoustic boundary conditions
1 Introduction In this paper, we are concerned with the following a quasi-nonlinear viscoelastic wave equation with acoustic boundary conditions: t ut(t) ρutt(t) – u(t) + g(t – s) u(s) ds
The functions f, q, h : 1 → R+ are essentially bounded. They studied the global nonexistence of solutions for a quasilinear wave equation with acoustic boundary conditions
Summary
System (1)–(6) is a model of a quasilinear viscoelastic wave equation with acoustic boundary conditions. Boukhatem and Benabderrahmane [2, 3] studied the existence, blow-up, and decay of solutions for viscoelastic wave equations with acoustic boundary conditions.
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