Asymptotic Behavior For Stochastic Ginzburg-Landau Equations

Complex Ginzburg-Landau equation,which is an important model in non-linear science,plays a fundamental role in various branches of Physics.Random attractor is the essential concept in studying the asymptotic behavior of random dynamical system.In this paper,we will consider the asymptotic behavior for complex Ginzburg-Landau equation with high order term in L2 and non-autonomous stochastic discrete complex Ginzburg-Landau equations in l?2 and l?p.In Chapter 1,we first introduce the background of random dynamical systems and gener-alized Ginzburg-Landau equations.At last we present our main work.In Chapter 2,we give the basic concepts and some Lemmas of random dynamical attractor and some inequalities that will be used in the paper.In Chapter 3,it is devoted to proving the asymptotic behavior for genenralized 2D Ginzburg-Landau equation with multiplicative noise.At first,we deal with the multiplica-tive noise terms.And then,with the Holder and Young inequalities and Gronwall Lemma,we obtain the existence of absorbing set in H and V.At last,we prove the existence of random attractor of random dynamical system associated with the equation in L2.In Chapter 4,it is devoted to proving the asymptotic behavior of non-autonomous stochas-tic discrete complex Ginzburg-Landau equations with additive noise.We prove the existence and uniqueness of the random attractor in a weighted space containing all bounded sequences.In addition,when deterministic external forcing terms are periodic in time,we show the random attractors are pathwise periodic.In Chapter 5,it is devoted to proving the asymptotic behavior of non-autonomous stochas-tic discrete complex Ginzburg-Landau equations with additive noise in weighted space e_p~p.In Chapter 6,we summarize our results and propose some works for future consideration.