Stochastic homogenization of the Keller–Segel chemotaxis system

Anastasios Matzavinos, Mariya Ptashnyk

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)58-76
Number of pages19
JournalNonlinear Analysis, Theory, Methods and Applications
Volume144
Early online date4 Jul 2016
DOIs
Publication statusPublished - Oct 2016

Keywords

  • Chemotaxis
  • Palm measures
  • Point processes
  • Stochastic homogenization
  • Two-scale convergence

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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