Stochastic homogenization of the Keller–Segel chemotaxis system. (October 2016)

• Record Type: Journal Article
• Authors: Matzavinos, Anastasios; Ptashnyk, Mariya
• Is Part Of: Nonlinear analysis. Volume 144(2016)
• Page Start: 58
• Page End: 76
• Publication Date: 2016-10
• Subjects: Chemotaxis -- Stochastic homogenization -- Two-scale convergence -- Palm measures -- Point processes; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.06.003
• Languages: English
• ISSNs: 0362-546X

Abstract

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 diffusion and chemotaxis coefficients for the chemotactic species is required. Finally, we prove the convergence of a periodization procedure for approximating the homogenized macroscopic coefficients.