Random Attractors For A Class Of Stochastic Fractional Wave Equations

Random attractor is an important concept which is used to describe the asymptotic behavior of random dynamical system.The main work of this paper is to consider the asymptotic property for stochastic fractional wave equations.Firstly,we transform the partial differential equation into the random equation that only contains the random parameters.Then we derive uniform prior estimates of solutions.Note that we prove the asymptotic compactness of the random dynamical system by using the energy equation method on bounded domains and the splitting technique on unbounded domains.At last,the existence of random attractors for stochastic wave equations is obtained.This paper is organized as follows:In Chapter 1,we introduce some research backgrounds on random dynamical system and stochastic fractional wave equations,then we state the main work of this paper.In Chapter 2,we give the concepts on random dynamical system and random attractor,some lemmas,theorems and inequalities that will be used in estimating.In Chapter 3,we study the non-autonomous stochastic wave equation with additive noise,and prove the existence of random attractor.In Chapter 4,we consider the stochastic fractional wave equations with additive noise on unbounded domains,and the existence of random attractors is obtained.In Chapter 5,we discuss the random attractors for stochastic fractional wave equations with dynamical boundary conditions.In Chapter 6,we conclude the works in our paper and give some plans on our future research.