UPPER SEMI-CONTINUITY OF RANDOM ATTRACTORS FOR A NON-AUTONOMOUS DYNAMICAL SYSTEM WITH A WEAK CONVERGENCE CONDITION

doi:10.1007/s10473-020-0403-3

Abstract

Abstract: In this paper, we develop the criterion on the upper semi-continuity of random attractors by a weak-to-weak limit replacing the usual norm-to-norm limit. As an application, we obtain the convergence of random attractors for non-autonomous stochastic reaction-diffusion equations on unbounded domains, when the density of stochastic noises approaches zero. The weak convergence of solutions is proved by means of Alaoglu weak compactness theorem. A differentiability condition on nonlinearity is omitted, which implies that the existence conditions for random attractors are sufficient to ensure their upper semi-continuity. These results greatly strengthen the upper semi-continuity notion that has been developed in the literature.

Key words: non-autonomous random dynamical system, random attractor, upper semi-continuity, weak convergence

CLC Number:

35R60

Wenqiang ZHAO, Yijin ZHANG. UPPER SEMI-CONTINUITY OF RANDOM ATTRACTORS FOR A NON-AUTONOMOUS DYNAMICAL SYSTEM WITH A WEAK CONVERGENCE CONDITION[J].Acta mathematica scientia,Series B, 2020, 40(4): 921-933.

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