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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 981576, 16 pages
Research Article

Random Attractors for Stochastic Retarded Reaction-Diffusion Equations on Unbounded Domains

1School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang, Henan 471023, China
2School of Mathematics and Science, Shanghai Normal University, Shanghai 200234, China

Received 10 March 2013; Accepted 28 May 2013

Academic Editor: Grzegorz Lukaszewicz

Copyright © 2013 Xiaoquan Ding and Jifa Jiang. 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.


This paper is devoted to a stochastic retarded reaction-diffusion equation on all -dimensional space with additive white noise. We first show that the stochastic retarded reaction-diffusion equation generates a random dynamical system by transforming this stochastic equation into a random one through a tempered stationary random homeomorphism. Then, we establish the existence of a random attractor for the random equation. And the existence of a random attractor for the stochastic equation follows from the conjugation relation between two random dynamical systems. The pullback asymptotic compactness is proved by uniform estimates on solutions for large space and time variables. These estimates are obtained by a cut-off technique.