Advances in Difference Equations
Volume 2010 (2010), Article ID 357404, 12 pages
doi:10.1155/2010/357404
Research Article

Exponential Decay of Energy for Some Nonlinear Hyperbolic Equations with Strong Dissipation

Yaojun Ye

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

Received 14 December 2009; Revised 21 May 2010; Accepted 4 August 2010

Academic Editor: Tocka Diagana

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 equations with strong dissipative term utt-∑i=1n(∂/∂xi)(|∂u/∂xi|p-2(∂u/∂xi))-aΔut=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 showing the exponential decay of the energy of global solutions through the use of an important lemma of V. Komornik.