Wenqiang Zhao, Shuzhi Song
Abstract:
This article concerns the dynamics of stochastic nonclassical diffusion
equation on
perturbed by a
-random
term, where
is the intension of noise.
By using an energy approach, we prove the asymptotic compactness of the
associated random dynamical system, and then the existence of random
attractors in
.
Finally, we show the upper semi-continuity
of random attractors at
in the sense of Hausdorff semi-metric in
,
which implies that the obtained family of random
attractors indexed by
converge to a deterministic attractor
as
vanishes.
Submitted April 27, 2015. Published November 10, 2015.
Math Subject Classifications: 60H15, 35B40, 35B41.
Key Words: Stochastic nonclassical diffusion equation; random attractor;
asymptotic compactness; weak continuity; upper semi-continuity.
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Wenqiang Zhao School of Mathematics and Statistics Chongqing Technology and Business University Chongqing 400067, China email: gshzhao@sina.com | |
Shuzhi Song School of Mathematics and Statistics Chongqing Technology and Business University Chongqing 400067, China email: 13718903@qq.com |
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