Existence, Nonexistence and Decay Estimate of Global Solutions for a Viscoelastic Wave Equation with Nonlinear Boundary Damping and Internal Source Terms

Abstract

In this paper, we consider the initial boundary value problem for a viscoelastic wave equation with nonlinear boundary damping and internal source terms. We first prove the existence of global weak solutions by the combination of Galerkin approximation, potential well and monotonicity-compactness methods. Then, we give an explicit decay rate estimate of the energy by making use of the perturbed energy method. Finally, the finite time blow up result of the solutions is investigated under certain assumptions on the relaxation function g and initial data.