| This paper investigate the existence and upper semicontinuity of random attractors for stochastic reaction-diffusion equations with distribution derivatives and additive noise perturbation.Firstly,we prove that the Reaction-Diffusion equations generate a continuous stochastic dynamic system through Galerkin’s approximations.Secondly,by using uniform a priori estimates for the far field value of the solution,we demonstrate that the dynamic system is asymptotic compact.Finally,the(L2(Rn),Lp(Rn))-random attractor is obtained.Particularly,we have weaken conditions for those semilinear Reaction-Diffusion equations while we obtain more generalized conclusions.In the first chapter,we introduce the background and present the situation of attractors of reaction-diffusion equation and introduce some symbols.In the second chapter,we review some basic concepts and properties related to this paper,and then introduce inequalities that will be used frequently in the derivation of this paper.In the third chapter,a dynamic system is derived from the reaction-diffusion equation with additive noise and distribution derivatives in an unbounded domain.In the forth chapter,we estimate each part of the solution and prove the existence of absorbing set.In the fifth chapter,we prove the asymptotic compactness of dynamical systems and obtain a(L2(Rn),Lp(Rn))-random attractor,then we study the upper semicontinuity of(L2(Rn),Lp(Rn))-random attractor. |
