Abstract and Applied Analysis
Volume 2013 (2013), Article ID 578345, 20 pages
http://dx.doi.org/10.1155/2013/578345
Research Article

Existence and Asymptotic Behavior of Traveling Wave Fronts for a Time-Delayed Degenerate Diffusion Equation

Weifang Yan and Rui Liu

Department of Mathematics, South China University of Technology, Guangzhou 510640, China

Received 15 November 2012; Revised 15 February 2013; Accepted 18 February 2013

Academic Editor: Peixuan Weng

Copyright © 2013 Weifang Yan and Rui 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 is concerned with traveling wave fronts for a degenerate diffusion equation with time delay. We first establish the necessary and sufficient conditions to the existence of monotone increasing and decreasing traveling wave fronts, respectively. Moreover, special attention is paid to the asymptotic behavior of traveling wave fronts connecting two uniform steady states. Some previous results are extended.