The Existence Of Attractors For Stochastic Ginzburg-Landau Equations

Let0be an open bounded domain in R2with sufficiently regular boundary. We consider the asymptotic behavior of the following stochastic Ginzburg-Landau equationWhere λ, α, v, k,β, σ∈R, k>|β|, λ>0.f is forced items, X is random items.This paper is divided into two parts. In the first part. when f depends on the time order to study the dynamics behavior of non-autonomous stochastic equation, first of all,we introduce dynamical system generated by the above equation with two parameters. Then, we prove the existence of absorbing set.After that, we prove the pullback asymptotic compactness of the equation with the idea of energy equations as introduced by Ball to solutions, Finally we prove the existence of pullback attractors in the phase space of L2(O). Markov process,thus,Studying stochastic differential equations driven by fractional Brown Motion can not use the method of the process of Wiener.we adopt the concept of fractal integral and its related result, and then calculation is different, under appropriate conditions, by using the methed of prior estimate,we have proved the existence of the attractor of the above equation.