Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 394859, 14 pages
Research Article

Existence and Asymptotic Behavior of Global Solutions for a Class of Nonlinear Higher-Order Wave Equation

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

Received 5 November 2009; Accepted 28 January 2010

Academic Editor: Marta García-Huidobro

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.


The initial boundary value problem for a class of nonlinear higher-order wave equation with damping and source term utt+Au+a|ut|p1ut=b|u|q1u in a bounded domain is studied, where A=(Δ)m, m1 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.