A general stability result for second order stochastic quasilinear evolution equations with memory

Abstract

Abstract The goal of this paper is to discuss an initial boundary value problem for the stochastic quasilinear viscoelastic evolution equation with memory driven by additive noise. We prove the existence of global solution and asymptotic stability of the solution using some properties of the convex functions. Moreover, our result is established without imposing restrictive assumptions on the behavior of the relaxation function at infinity.

Keywords

• Quasilinear stochastic viscoelastic wave equations
• Explosive solutions
• Energy inequality