Homogenization of random parabolic operators. Diffusion approximation

TL;DR

This paper investigates the homogenization of random parabolic operators with periodic spatial and stationary temporal coefficients, analyzing the asymptotic behavior of solution differences under self-similar diffusion scaling.

Contribution

It provides new insights into the limit behavior of solutions to homogenized parabolic operators with mixed periodic and random coefficients under specific scaling regimes.

Findings

Asymptotic behavior depends on spatial-temporal scaling ratio

Results apply to self-similar parabolic diffusion scaling

Provides conditions under which homogenization limits are characterized

Abstract

The paper deals with homogenization of divergence form second order parabolic operators whose coefficients are periodic in spatial variables and random stationary in time. Under proper mixing assumptions, we study the limit behaviour of the normalized difference between solutions of the original and the homogenized problems. The asymptotic behaviour of this difference depends crucially on the ratio between spatial and temporal scaling factors. Here we study the case of self-similar parabolic diffusion scaling.