Random Attractors For A Class Of Stochastic Fractional Reaction-Diffusion Equations

Stochastic reaction-diffusion equation is one of the most important models in mathematical physics and plays an important role in many fields,such as physics,biology and chemistry.In this thesis,the main work is to discuss the random attractors for a class of stochastic fractional reaction-diffusion equations.Firstly,we transform the stochastic partial differential equations into new random equations.Then,the existence and uniqueness of random attractors can be obtained by deriving uniform estimates of solutions for the equations and the compact embedding theorem.Finally,we prove the boundedness of the fractal dimension of the random attractors by using the decomposition technique and estimating the boundedness of expectation of some random variables.This thesis is organized as follows:In Chapter 1,we introduce the basic concepts of random dynamical system,the research background and present progress of random fractional reaction-diffusion equations,and briefly describe the main work of this thesis.In Chapter 2,we give some concepts and theorems of random attractors and random dynamical system,and sufficient conditions to prove the finite fractal dimension of random attractors.In Chapter 3,we study the non-autonomous stochastic fractional reaction-diffusion equation on bounded domains driven by multiplicative noise,and prove the existence of random attractors and the boundedness of fractal dimension of the random attractors.In Chapter 4,we consider the stochastic fractional reaction-diffusion equation on bounded domains by additive noise,and prove the existence of random attractors and the boundedness of fractal dimension of the random attractors.