(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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Published in | Abstract and Applied Analysis Vol. 2013; no. 2013; pp. 792 - 814-277 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Cairo, Egypt
Hindawi Limiteds
01.01.2013
Hindawi Puplishing Corporation Hindawi Publishing Corporation John Wiley & Sons, Inc Hindawi Limited |
Subjects | |
Online Access | Get full text |
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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. |
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ISSN: | 1085-3375 1687-0409 |
DOI: | 10.1155/2013/279509 |