Upper Semicontinuity Of Pullback Attractors For The Stochastic Reaction-diffusion Equation With The Rapidly Oscillating Forcing Term

In this paper,we mainly study the existence and upper semicontinuity of an pullback attractors for non-autonomous stochastic reaction-diffusion equation with the rapidly oscillating forcing terms on L2(Rn).We will consider the following s-tochastic equation with the rapidly oscillating forcing terms:(?)with the rapidly oscillating forcing terms g?(x,t):= g(x,t,t/?),(??(0,1]).Where ? is a positive constant.T?R,t>T and x ?Rn,g?(x,t)? Lloc2(R,L2(Rn)),W(t)is a two-sided real-valued Wiener process on a probability space(?,F,P),we write = {??C(R,R):?(0)= 0},let F be the Borel ?-algebra induced by the compact-open topology of ?,and P be the corresponding Wiener measure on(?,F).This paper is divided into four parts:The first chapter,this paper briefly introduces the background of the random dynamical system,non-autonomous dynamical systems,pullback attractor and the current research status of the existence and upper semicontinuity of the pullback attractor,then there contains some theories and results regarding pullback attractors for the random dynamical system over two parametric spaces.The second chapter,by using O-U process to eliminate the random disturbance and get the corresponding non-autonomous one,we get the existence of a continuous cocycle in L2(Rn)for the stochastic reaction-diffusion equation.The third chapter,we prove the existence of the bounded absorbing set and uniform asymptotically compactness of the system in L2(Rn)by using uniform es-timates on the tails of functions.And we get the existence and the uniqueness of pullback attractors.The forth chapter,we establish the upper semicontinuity of pullback attractors by the convergence of random dynamical system in L2(Rn).