On the Periodic Homogenization of the Maxwell–Stefan Equations

In this paper, the problem of periodic homogenization of the Maxwell-Stefan cross-diffusion system was studied in the case of three species with two equal binary diffusion coefficients. Using the technique of two-scale homogenization, we characterized the limit equation. The limit equation allows one to describe the behavior of a gas mixture in the diffusive regime in a porous medium. This paper provides the first rigorous mathematical results on the homogenization of the Maxwell--Stefan equations.