Stochastic homogenization of the Keller-Segel chemotaxis system

Abstract

In this paper, we focus on the Keller-Segel chemotaxis system in a random heterogeneous domain. We assume that the corresponding diffusion and chemotaxis coefficients are given by stationary ergodic random fields and apply stochastic two-scale convergence methods to derive the homogenized macroscopic equations. In establishing our results, we also derive a priori estimates for the Keller-Segel system that rely only on the boundedness of the coefficients; in particular, no differentiability assumption on the coefficients is required. Finally, we prove the convergence of a periodization procedure for approximating the homogenized asymptotic coefficients.