Abstract and Applied Analysis
Volume 2012 (2012), Article ID 615345, 27 pages
http://dx.doi.org/10.1155/2012/615345
Research Article

On Existence, Uniform Decay Rates, and Blow-Up for Solutions of a Nonlinear Wave Equation with Dissipative and Source

Xiaopan Liu

Department of Mathematics, Southeast University, Nanjing 210018, China

Received 24 May 2012; Revised 17 July 2012; Accepted 17 July 2012

Academic Editor: Narcisa C. Apreutesei

Copyright © 2012 Xiaopan Liu. 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

This paper studies the blow-up and existence, and asymptotic behaviors of the solution of a nonlinear hyperbolic equation with dissipative and source terms. By using Galerkin procedure and the perturbed energy method, the local and global existence of solution is established. In addition, by the concave method, the blow-up of solutions can be obtained.