Existence And Upper Semi-continuity Of Pullback Attractors For Non-autonomous Semi-linear Degenerate Parabolic Equations With Fast Oscillating Term

This paper introduces the non-autonomous semi-linear degenerate parabolic equations with fast oscillating ter.It mainly studies that the random dynamical system generated by the unique solution of corresponding problem exists a pullback attractor in L2(Rn)space,which is upper semi-continuous.The paper investigates the following non-autonomous semi-linear degenerate parabolic equations:where ? is a positive constant,g?(x,t)?Lloc2"o"is Stranovich integration.Random function W(t)is a two-sided real-valued Wiener-process on a prob-ability space(?,F,P,(?t)t?R),where ?= {??C(R,R):?(0)= 0},F is the Borel?-algebra induced by the compact-open topology of ?.P is a Wiener measure,for???,and t ? R,0 satisfies ?t?(·)= ?(· + t)-?(t).The non-linearityf(x,·)satisfy the assumption(F):Generally,?(x)? Lloc1.In this paper,we assume a(x)? Lloc1? L? because of the proving of theorem 3.2.2.The paper contains four chapters:In the first chapter:we introduce the background and the research status of RDS,random attractor and semi-linear degenerate parabolic equations,this paper'main contents and significance,also provides some relevant basic knowledge.In the second chapter:there is no stochastic differential for introducing O-U transformation.The unique solution of the equation by using the Galerkin approx-imate method is obtained,which generates a continue random dynamical system.In the third chapter:we get the unique random attractor in L2(Rn)space by uniform estimates of solutions and proving that there exist random absorbing sets both in L2(Rn)and D01,2(Rn,?)space,which combines with Sobolev compact embedding theory.In the fourth chapter:by the convergence of random dynamical system in L2(Rn)space,the upper semi-continuity of random attractor for the Semi-linear Degenerate Parabolic equations is obtained.