Stochastic homogenization of the Keller-Segel chemotaxis system

Anastasios Matzavinos, Mariya Ptashnyk

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Abstract

In this paper, we focus on the Keller-Segel chemotaxis system in a random heteroge-neous domain. We assume that the corresponding diffusion and chemotaxis coefficients are given by stationary ergodic random fields and apply stochastic two-scale conver-gence 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
Volume144
Early online date4 Jul 2016
DOIs
Publication statusPublished - Oct 2016

Keywords

  • Chemotaxis
  • stochastic
  • homogenization
  • two-scale convergence
  • Palm measures
  • point processes

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