Existence and decay of solutions for a viscoelastic wave equation with acoustic boundary conditions

Abstract

In this paper we consider a multi-dimensional damped semilinear viscoelastic wave equation with variable coefficient and acoustic boundary conditions. First, we prove a local existence theorem by using the Faedo–Galerkin approximations combined with a contraction mapping theorem. Second, we show that, under suitable conditions on the initial data and the relaxation function, the solution exists globally in time and we prove the uniform decay rate of the energy.