David Aristoff's homepage Title: Homogenization of stochastic and heterogenous models in porous media

Abstract: we study models with microscale properties that are highly heterogeneous in space and time. The time variations are controlled by a stochastic particle dynamics described by a stochastic differential equation (SDE). Our main results include the derivation of macroscale equations and showing that the macroscale equations are deterministic. The macro scale equations are derived through an averaging principle of the slow motion (fluid velocity) with respect to the fast motion (particle dynamics) and also by averaging some coefficient with respect to the space variable. Our results include some Brinkman flows and can be extended to more general nonlinear diffusion equations with heterogeneous coefficients.