Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 216760, 15 pages
Research Article

Global Existence, Uniqueness, and Asymptotic Behavior of Solution for p-Laplacian Type Wave Equation

Department of Mathematics, Hohai University, Nanjing, Jiangsu, 210098, China

Received 10 May 2010; Accepted 13 July 2010

Academic Editor: Michel C. Chipot

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.


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 uttdiv(|u|p2u)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|α1ub(x)|u|β1u with appropriate functions a(x) and b(x), where α>β1.