Homogenization of a singular random one dimensional parabolic PDE with time varying coefficients

摘要

The paper studies homogenization problem for a non-autonomous parabolicequation with a large random rapidly oscillating potential in the case of onedimensional spatial variable. We show that if the potential is a statisticallyhomogeneous rapidly oscillating function of both temporal and spatial variablesthen, under proper mixing assumptions, the limit equation is deterministic andthe convergence in probability holds. To the contrary, for the potential havinga microstructure only in one of these variables, the limit problem isstochastic and we only prove the convergence in law.