Asymptotic Behavior Of Stochastic Fractional Integro-differential Equations

In this thesis,we study the well-posedness and asymptotic behavior of fractional stochastic integro-differential equations in materials with memory.We first study the well-posedness and the existence of random attractors for the fractional stochastic integrodifferential equations in materials with memory on a bounded domain,then discuss the existence of random attractors and the upper semicontinuity of non-autonomous fractional stochastic integro-differential equations in materials with memory.Due to the fact that the memory term takes into account the whole past history of the phenomenon,we are not able to prove compactness of the generated RDS,but its asymptotic compactness can be proved by the splitting method,ensuring thus the existence of the random pullback attractor.This thesis is organized as follows:In Chapter 1,we introduce the backgrounds and research progresses of the equations,and give main works of this paper.In Chapter 2,we present some basic notions and theories that will be used in this thesis.In Chapter 3,we first apply the Galerkin method to prove the existence and uniqueness of solutions for the equation,then establish the existence and uniqueness of tempered pullback random attractors.In Chapter 4,we study the asymptotic behavior of non-autonomous fractional stochastic integro-differential equations in materials with memory.We first prove the existence of random attractors and then the upper semicontinuity is obtained when the intensity of noise approaches zero.