Pullback Attractors Of Stochastic Reaction-Diffusion Equations With General Noise On Thin Domains

This paper is concerned with the attractors of stochastic reaction-diffusion e-quations with general noise and deterministic non-autonomous terms defined on thin domains,we first prove the existence,uniqueness,and periodicity of the random attractor for the stochastic dynamic system which is generated by the solution of the equation in an(n+l)-dimension thin domain,after that,we establish the up-per semicontinuity of these attractors when the family of(n+1)-dimensional thin domains collapses to n-dimensional domain.Let Q ? Rn be a bounded domain and O??R(n+1)(be the domain where(?),which implies that there exist positive constants r1 and r2 such that we write (?).we consider the following equation:with initial condition the stochastic equation is understood in the sense of Straronovich integration,where W is a general two-sided real-valued stochastic process defined on a general proba-bility space(?,F,P)?? R,v? is the unit outward vector on(?)O?,G is a function defined on (?).f is a nonlinear function defined on (?).The following briefly introduces the content structure of this articleFirstly,We briefly describe the history and important branches of the dynam-ical system,and then introduce the research background and current status of the stochastic reaction-diffusion equations and pullback attractor on thin domain.We also Explain this paper's main contents and significanceThen in the second chapter,we provides some relevant basic knowledge,and consider with the continuous stochastic dynamic system generated by the reaction-diffusion equation with general noise on an thin domain.First,we use the domain transformation to transfer the problem of the solution for the equation on an thin domain into boundary value problems the fixed domain,after that,we convert the stochastic equation into a deterministic one with parameters.Then according to the Galerkin theorem,it is proved that the stochastic reaction diffusion equation has a unique solution on L2(O),and a continuous cocycle can be generated by using this unique solution.After that,we derive uniform estimates of the solution for the equation in the space Hg(O),which are needed for proving the existence of pullback absorbing set.Thanks to the compact embedding theorem,the cocycle is D-pullback asymptoti-cally compact in L2(O).Hence,the existence of a unique pullback attractor follows form Theorem 3.1 immediatelyFinally,we derive the upper-semicontinuity of pullback attractors by the con-vergence of random dynamical system in L2(O)space.