Global existence and blow up of positive initial energy solution of a quasilinear wave equation with nonlinear damping and source terms

Abstract

In this paper, we consider a quasilinearwave equation having nonlinear damping and source terms utt−Δut−∑i=1n∂∂xiσi(x, uxi)+β(x, utxi)+f(x, ut)=g(x, u) and obtained global existence and blow up results under certain polynomial growth conditions on the nonlinear functions σi, βi, (i = 1, 2, ..., n), f and g. We obtain global existence result for positive initial energy solution using Galerkin approximation procedure and nonexistence (blow up) result using the technique introduced by Georgiev and Todorova (1994) with little modification for our problem.