Homogenization of a random non-stationary convection-diffusion problem

Abstract

The homogenization problem is studied for a non-stationary convection-diffusion equation with rapidly oscillating coefficients periodic in the spatial variables and stationary random in the time. Under the assumption that the coefficients of the equation have rather good mixing properties, it is shown that, in properly chosen moving coordinates, the distribution of the solution of the original problem converges to the solution of the limit stochastic partial differential equation. The homogenized problem is well-posed and determines the limit measure uniquely.