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 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 is proved by the well-known tail estimate technique and the estimate of the integral of -norm of truncation of solutions over a compact interval.
Submitted September 4, 2016. Published November 16, 2016.
Math Subject Classifications: 60H15, 60H30, 60H40, 35B40, 35B41.
Key Words: Random dynamical systems; upper semi-continuity; non-autonomous reaction-diffusion equation; pullback attractor.
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| Wenqiang Zhao |
School of Mathematics and Statistics
Chongqing Technology and Business University
Chongqing 400067, China
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