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Abstract and Applied Analysis
Volume 2011 (2011), Article ID 142128, 13 pages
http://dx.doi.org/10.1155/2011/142128
Research Article

On Asymptotic Behavior for Reaction Diffusion Equation with Small Time Delay

School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, China

Received 11 October 2011; Revised 5 November 2011; Accepted 5 November 2011

Academic Editor: Elena Litsyn

Copyright © 2011 Xunwu Yin. 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

We investigate the asymptotic behavior of scalar diffusion equation with small time delay ut-Δu=f(ut,u(t-τ)). Roughly speaking, any bounded solution will enter and stay in the neighborhood of one equilibrium when the equilibria are discrete.