Abstract and Applied Analysis

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

Xiaoquan Ding and Jifa Jiang

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Abstract

This paper is devoted to a stochastic retarded reaction-diffusion equation on all d -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.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 981576, 16 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393511981

Digital Object Identifier
doi:10.1155/2013/981576

Mathematical Reviews number (MathSciNet)
MR3081613

Zentralblatt MATH identifier
07095556

Citation

Ding, Xiaoquan; Jiang, Jifa. Random Attractors for Stochastic Retarded Reaction-Diffusion Equations on Unbounded Domains. Abstr. Appl. Anal. 2013 (2013), Article ID 981576, 16 pages. doi:10.1155/2013/981576. https://projecteuclid.org/euclid.aaa/1393511981


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