带加性噪声的分数阶随机Ginzburg-Landau方程的渐近行为

Asymptotic Behavior of the 2D Generalized Fractional Stochastic Ginzburg-Landau Equation with Additive Noise

考虑带加性噪声的随机分数阶Ginzburg-Landau方程在L^2(D)中的渐近性质.首先将随机偏微分方程转化为仅含随机参数的随机方程,然后对该方程的解进行先验估计,从而得到随机动力系统的紧性,最后证明L^2(D)中随机吸引子的存在性.

In this paper,the asymptotic dynamic problem is considered for the fractional stochastic Ginzburg-Landau equation with additive noise defined in L^2（D）. Firstly,the partial differential equation is trasformed into the random equation that only includes the random parameters. The compactness of the random dynamical system then is established by a priori estimation method. And finally,the existence of a random attractor for the random dynamical system is proved in L^2（D）.