Copyright © 2010 Caisheng Chen et al. 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

We study the global existence and uniqueness of a solution to an initial boundary value problem for the nonlinear wave equation with the p-Laplacian operator utt−div(|∇u|p−2∇u)−Δut+g(x,u)=f(x). Further, the asymptotic behavior of solution is established. The nonlinear term g likes g(x,u)=a(x)|u|α−1u−b(x)|u|β−1u with appropriate functions a(x) and b(x), where α>β≥1.