Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 597569, 12 pages
Research Article

Asymptotic Behavior of Solutions of a Periodic Diffusion Equation

Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Received 25 September 2009; Accepted 24 December 2009

Academic Editor: Shusen Ding

Copyright © 2010 Jiebao Sun et al. 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.


We consider a degenerate parabolic equation with logistic periodic sources. First, we establish the existence of nontrivial nonnegative periodic solutions by monotonicity method. Then by using Moser iterative technique and the method of contradiction, we establish the boundedness estimate of nonnegative periodic solutions, by which we show that the attraction of nontrivial nonnegative periodic solutions, that is, all non-trivial nonnegative solutions of the initial boundary value problem, will lie between a minimal and a maximal nonnegative nontrivial periodic solutions, as time tends to infinity.