Random Attractor For Stochastic Fractional Ginzburg-landau Equations

As we know,the random attractor is the essential concept which is used to describe the asymptotic behavior of random dynamical system.We consider the asymptotic property for stochastic fractional Ginzburg-Landau equations.We transform the partial differential equation into the stochastic equation that only contains the random parameters.Then,using estimates for far-field values of solutions and a cut-off technique,asymptotic compactness is proved.At last,the existence of a random attractor for the stochastic fractional GinzburgLandau equation is obtained.This paper is organized as follows:In the first chapter,we introduce some research backgrounds on random dynamical system and stochastic fractional Ginzburg-Landau equation,and the main work of this paper.In the second chapter,we give the concepts on random dynamical system and random attractors,some lemmas,theorems and inequalities that will be used in estimation.In the third chapter,we study the stochastic fractional Ginzburg-Landau equation with multiplicative noise,and prove the existence of random attractors.In the fourth chapter,the stochastic fractional Ginzburg-Landau equations with additive noise on unbounded domains is studied,and the existence of random attractors is got.In the fifth chapter,we discuss the stochastic fractional non-autonomous Ginzburg-Landau equations with multiplicative noise in weighted space,and obtain the existence of random attractors.In the sixth chapter,we conclude the works in our paper and give some further consideration on our next research.