一类随机抛物型偏微分方程的噪声影响分析

Effectiveness of Noises for a Class of Stochastic Parabolic PDEs

考虑一类带动态边值的随机抛物型偏微分方程.白噪声不仅出现在系统模型中,同时出现在边值条件中.证明了当系统的噪声强度趋近零时,该系统的随机不变流几乎必然收敛到其对应的确定系统的确定不变流.

This paper is concerned with a class of stochastic parabolic partial differential equations with dynamical boundary condition.The white noises act both in the model and in the dynamical boundary condition.The purpose of the paper is to prove that when the intensity of white noises tends to zero,the stochastic invariant manifold converges to its deterministic counterpart almost surely.