On a system of nonlinear wave equations with Balakrishnan–Taylor damping

Abstract

In this paper, we study the initial-boundary value problem for a coupled system of nonlinear viscoelastic wave equations of Kirchhoff type with Balakrishnan–Taylor damping terms. For certain class of relaxation functions and certain initial data, we prove that the decay rate of the solution energy is similar to that of relaxation functions which is not necessarily of exponential or polynomial type. Also, we show that nonlinear source of polynomial type is able to force solutions to blow up in finite time even in presence of stronger damping.