Homogenization in a periodic and time-dependent potential

Abstract. This paper contains a study of the long time behavior of a diffusion process in a periodic potential. The first goal is to determine a suitable rescaling of time and space so that the diffusion process converges to some homogeneous limit. The issue of interest is to characterize the effective evolution equation. The main result is that in some cases large drifts must be removed in order to get a diffusive asymptotic behavior. This is applied to the homogenization of parabolic differential equations. Key words. homogenization, partial differential equations in media with periodic structure, diffusion processes AMS subject classifications. 35B27, 60J60 PII. S003613999528200