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

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  • Xiaoquan Ding
  • Jifa Jiang

Abstract

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.

Suggested Citation

  • Xiaoquan Ding & Jifa Jiang, 2013. "Random Attractors for Stochastic Retarded Reaction-Diffusion Equations on Unbounded Domains," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-16, July.
    • Handle: RePEc:hin:jnlaaa:981576
    DOI: 10.1155/2013/981576
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