Existences and upper semi-continuity of pullback attractors in H^1(R^N) for non-autonomous reaction-diffusion equations perturbed by multiplicative noise

In this article, we establish sufficient conditions on the existence and upper semi-continuity of pullback attractors in some non-initial spaces for non-autonomous random dynamical systems. As an application, we prove the existence and upper semi-continuity of pullback attractors in $H^1(\mathbb{R}^...

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Bibliographic Details
Published inElectronic journal of differential equations Vol. 2016; no. 294; pp. 1 - 28
Main Author Wenqiang Zhao
Format Journal Article
LanguageEnglish
Published Texas State University 16.11.2016
Subjects
non-autonomous reaction-diffusion equation
pullback attractor
Random dynamical systems
upper semi-continuity
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Summary:In this article, we establish sufficient conditions on the existence and upper semi-continuity of pullback attractors in some non-initial spaces for non-autonomous random dynamical systems. As an application, we prove the existence and upper semi-continuity of pullback attractors in $H^1(\mathbb{R}^N)$ are proved for stochastic non-autonomous reaction-diffusion equation driven by a Wiener type multiplicative noise as well as a non-autonomous forcing. The asymptotic compactness of solutions in $H^1(\mathbb{R}^N)$ is proved by the well-known tail estimate technique and the estimate of the integral of $L^{2p-2}$-norm of truncation of solutions over a compact interval.
ISSN:1072-6691