DMS Analysis and Stochastic Analysis Seminar (SASA)

Speaker: Yuming Paul Zhang (Auburn University)

Title: Stochastic homogenization for reaction diffusion equations

Abstract: Homogenization is a general phenomenon observed in physical processes occurring within periodic or random environments, wherein the long-term dynamics exhibit homogeneity due to large-scale averaging of environmental variations. In this presentation, I will discuss stochastic homogenization for reaction-diffusion equations in multiple spatial dimensions. To address environments that may not satisfy the finite distance dependence condition (roughly speaking, non-i.i.d environment), we develop a generalized Azuma's inequality. Additionally, our discussion will encompass various types of reaction functions.