(L2, H1)‐Random Attractors for Stochastic Reaction‐Diffusion Equation on Unbounded Domains

Gang Wang and Yanbin Tang

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: 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.

Date: 2013
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https://doi.org/10.1155/2013/279509

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:279509

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