Uniform decay of solutions for a quasilinear system of viscoelastic equations

Abstract

In this paper, we consider a system of two coupled quasilinear viscoelastic equations in canonical form with Dirichlet boundary condition. We use the perturbed energy method to show that the dissipations given by the viscoelastic terms are strong enough to ensure uniform decay (with exponential and polynomial rates) of the solutions energy, which extends some existing results for a single equation to the case of a coupled system.