Asymptotic Stability of the Viscoelastic Equation with Variable Coefficients and the Balakrishnan-Taylor Damping

Abstract

In this paper, we consider the viscoelastic equation with variable coefficients and Balakrishnan-Taylor damping and source terms. This work is devoted to prove, under suitable conditions on the initial data, the asymptotic stability without imposing any restrictive growth assumption on the damping term and weakening of the usual assumptions on the relaxation function.