From averaging to homogenization in cellular flows - an exact description of the transition

TL;DR

This paper investigates the transition from averaging to homogenization in cellular flows, providing an exact description of the process and a limit theorem for the associated diffusion, enhancing understanding of multiscale PDE behavior.

Contribution

It offers a rigorous limit theorem and a detailed characterization of the transition between averaging and homogenization in elliptic PDEs with cellular flows.

Findings

Derived a limit theorem for the diffusion process.

Provided a precise description of the two-parameter limit behavior.

Enhanced understanding of the transition in multiscale PDEs.

Abstract

We consider a two-parameter averaging-homogenization type elliptic problem together with the stochastic representation of the solution. A limit theorem is derived for the corresponding diffusion process and a precise description of the two-parameter limit behavior for the solution of the PDE is obtained.