带乘性噪声的随机分数阶Ginzburg-Landau方程的渐近行为

Asymptotic Behavior of the Stochastic Fractional Ginzburg-Landau Equation with Multiplicative Noise

考虑带乘性噪声的随机分数阶Ginzburg-Landau方程在L2(R)空间中的渐近性质.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,最后证明了L2(R)中随机吸引子的存在性.

In this paper,we consider the asymptotic dynamic for the fractional stochastic Ginzburg-Landau equation with multiplicative noise defined in L^2(R^2).Firstly,we transform the stochastic partial differential equation into the random equation that only contains the random parameter.Then,the compactness of the random dynamical system is established by a priori estimate for the solution,which shows the existence of a random attractor for the random dynamical system possesses in L^2(R^2).