Upper Semicontinuity Of Random Attractors For Stochastic P-Laplace Equations With Rapidly Oscillating External Force On Unbounded Domains

We consider the upper semicontinuity of random attractors for a stochastic p-Laplace equation with rapidly oscillating external force on Rn.The asymptotic compactness of attractors on unbounded domains is proved by means of the tail of the solution.We will investigate the following generalized p-Laplace equation:For t>?,??R:(?)where p>2,?>0,?>0.This paper is divided into four chapters:In the first chapter,we introduce the background on the theory of random dynamical system,random attractors and the research status of p-Laplace equa-tion,main contents of this paper;And we give some preliminary definitions and re-sults,which will be used.In the second chapter,there is no stochastic differential for introducing O-U transformation.The unique solution of the equation by using the Galerkin approxi-mate method is obtained,which generates a continuous random dynamical system.In the third chapter,we get the unique random attractor in L2(R)space by uni-form estimates of solutions and proving that there exist random absorbing sets both in L2(R)space and H01(R)space,which combines with Sobolev compact embedding theory.In the fourth chapter,by the convergence of random dynamical system in L2 space,upper semicontinuity of random attractor is obtained.