A Note on Homogenization of Advection-Diffusion Problems with Large Expected Drift

Abstract

This contribution is concerned homogenization of linear advection-diffusion problems with rapidly oscillating coefficient functions and large expected drift. Even though the homogenization of this type of problems is generally well known, there are several details that have not yet been treated explicitly or even not been treated at all. Here, we will have a special look at uniqueness, regularity, boundedness and equivalent formulations of the homogenized equation. In particular, we generalize results of Allaire and Raphael [C. R. Math. Acad. Sci. Paris 344 (2007)(8), 523–528] and Donato and Piatnitski [Multi Scale Problems and Asymptotic Analysis. Tokyo: Gakkotosho 2006, pp. 153–165]. The results obtained in this contribution are of special interest for the numerical analysis of multi-scale schemes to approximate the analytic solutions.