Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 895121, 10 pages
doi:10.1155/2010/895121
Research Article

Global Existence and Asymptotic Behavior of Solutions for Some Nonlinear Hyperbolic Equation

Yaojun Ye

Department of Mathematics and Information Science, Zhejiang University of Science and Technology, Hangzhou 310023, China

Received 14 December 2009; Accepted 18 March 2010

Academic Editor: Shusen Ding

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 hyperbolic equation with nonlinear dissipative term utt-∑i=1n(∂/∂xi)(|∂u/∂xi|p-2(∂u/∂xi))+a|ut|q-2ut=b|u|r-2u in a bounded domain is studied. The existence of global solutions for this problem is proved by constructing a stable set in W01,p(Ω) and show the asymptotic behavior of the global solutions through the use of an important lemma of Komornik.