The need to take stochastic effects into account for modeling complex systems has now become widely recognized. Stochastic partial differential equations arise naturally as mathematical models for multiscale systems under random influences. We consider macroscopic dynamics of microscopic systems described by stochastic partial differential equations. The microscopic systems are characterized by small scale heterogeneities (spatial domain with small holes or oscillating coefficients), fast scale boundary impact (random dynamic boundary condition), and, random fluctuations. 

An effective macroscopic model for such a stochastic microscopic system is derived.   The homogenized effective model is still a stochastic partial differential equation, but defined on a unified spatial  domain and the random impact is represented by an extra term in the effective model. The solutions of the microscopic model is shown to converge to those of the effective macroscopic model in probability distribution, as the size of holes diminishes to zero. Moreover, the long time effectivity of the macroscopic system in the sense of convergence in probability distribution, and in  the sense of convergence in energy are also proved.

简介： 段金桥教授任职于美国伊利诺理工学院应用数学系，是该校随机动力系统与非线性动力系统实验室主任。主要从事随机动力系统、随机偏微分方程、随机分析、随机系统的计算模拟、随机现象建模、分析和控制、多重尺度复杂随机系统的分析方法研究。

    欢迎参加！

清华大学周培源应用数学研究中心

唐 琳

TEL:62797063