Attractors Of A Class Of Generalized Stochastic Ginzburg-Landan Equations

Abstrct Random attractor is the essential concept in describing the asymptotic be-havior of random dynamical system. The present paper is devoted to the existence of therandom attractors of stochastic Ginzburg-Landau equations. In Chapter1, we take a brief view of the background of random dynamical systems andthe derivation for our general Ginzburg-Landau equations. Here, we present an overview ofour main work. In Chapter2, we give the introduction of the basic concepts of random attractors whichcontains some inequalities that will be used in the following. In Chapter3, it is devoted to proving the existence of the random attractors of stochasticGizburg-Landau equation with additive noise defined on a bounded domain. By establishingthe uniform estimate of the solution of the equation, we deduce the existence of a randombounded absorbing set. In Chapter4, we firstly prove the existence of a pullback attractor of a stochasticGinzburg-Landau equation with additive noise on unbounded domains. Then we deduce arandom differential equation with random coefficient from the stochastic equation by Ornstein-Uhlenbeck transformation. We convert the equation to a random dynamical system anddemonstrate the asymptotic compactness by using uniform estimates for far-field values ofsolutions. In Chapter5, we summarize our results and propose some works for future consideration.