奇异扰动的分数阶随机反应扩散方程的吸引子

Attractors for Fractional-order Stochastic Reaction-diffusion Equations with Multiplicative Noise and Singular Perturbation

研究了定义在光滑有界域O■R^(n)上、带乘性噪声和奇异扰动的分数阶随机反应扩散方程在L^(2)(O)上的随机拉回吸引子的存在性。由于奇异扰动和分数阶算子对系统的作用,无法用正则估计得到系统的紧性问题,因此利用Aubin紧性定理获得了由方程生成的随机动力系统的渐近紧性。

The existence of random pullback attractors on L^(2)(O)for fractional-order stochastic reaction-diffusion equations with multiplicative noise and singular perturbations defined over a smooth bounded domain O■R^(n)was investigated.Due to the effects of singular perturbations and fractional operators on the system,it was not possible to obtain the compactness of the system using regular estimation.Therefore,the Aubin compactness theorem was used to obtain the asymptotic compactness of the stochastic dynamical system generated by the equation.