Copyright © 2010 Yaojun Ye. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The initial boundary value problem for a class of nonlinear higher-order wave equation with damping and source term utt+Au+a|ut|p−1ut=b|u|q−1u in a bounded domain is studied, where A=(−Δ)m, m≥1 is a nature number, and a,b>0 and p,q>1 are real numbers. The existence of global solutions for this problem is proved by constructing the stable sets and shows the asymptotic stability of the global solutions as time goes to infinity by applying the multiplier method.