(L^2,H^1)-Random Attractors for Stochastic Reaction-Diffusion Equation on Unbounded Domains

We study the random dynamical system generated by a stochastic reaction-diffusion equation with additive noise on the whole space ℝn and prove the existence of an (L2,H1)-random attractor for such a random dynamical system. The nonlinearity f is supposed to satisfy the growth of arbitrary order p-1...

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Bibliographic Details
Published inAbstract and Applied Analysis Vol. 2013; no. 2013; pp. 792 - 814-277
Main Authors Wang, Gang, Tang, Yanbin
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Limiteds 01.01.2013
Hindawi Puplishing Corporation
Hindawi Publishing Corporation
John Wiley & Sons, Inc
Hindawi Limited
Subjects
Diffusion
Dynamical systems
Learning models (Stochastic processes)
Mathematical research
Noise
Stochastic models
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Summary:We study the random dynamical system generated by a stochastic reaction-diffusion equation with additive noise on the whole space ℝn and prove the existence of an (L2,H1)-random attractor for such a random dynamical system. The nonlinearity f is supposed to satisfy the growth of arbitrary order p-1 (p≥2). The (L2,H1)-asymptotic compactness of the random dynamical system is obtained by using an extended version of the tail estimate method introduced by Wang (1999) and the cut-off technique.
ISSN:1085-3375
1687-0409
DOI:10.1155/2013/279509