Global Existence and Uniform Decay of Solutions for a Coupled System of Nonlinear Viscoelastic Wave Equations with Not Necessarily Differentiable Relaxation Functions

Abstract

In this paper, we consider the initial boundary value problem for a coupled system of nonlinear viscoelastic wave equations with source terms. By using the Faedo–Galerkin method, potential well theory and perturbed energy technique, we establish the global existence and exponential decay of solutions under weaker conditions on the relaxation functions that are not necessarily differentiable.