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

作　　者：Wenqiang ZHAO Yijin ZHANG 赵文强;张一进(Chongqing Key Laboratory of Social Economy and Applied Statistics,School of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067,China;Chongqing Key Laboratory of Social Economy and Applied Statistics,School of Science,Chongqing University of Posts and Telecommunications,Chongqing 400065,China)

机构地区：[1]Chongqing Key Laboratory of Social Economy and Applied Statistics,School of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067,China [2]Chongqing Key Laboratory of Social Economy and Applied Statistics,School of Science,Chongqing University of Posts and Telecommunications,Chongqing 400065,China

出　　处：《Acta Mathematica Scientia》2020年第4期921-933,共13页数学物理学报（B辑英文版）

基　　金：CTBU(KFJJ2018101);CTBU ZDPTTD 201909;Chongqing NSF(2019jcyj-msxm X0115);NSFC(11871122).

摘　　要：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 reactiondiffusion 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.

关 键 词：non-autonomous random dynamical system random attractor upper semicontinuity weak convergence 

分 类 号：O211.63[理学—概率论与数理统计]