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arXiv · 1310.3430

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 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.

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Anastasios Matzavinos, Mariya Ptashnyk. 2013-10-12. Stochastic homogenization of the Keller-Segel chemotaxis system. https://doi.org/10.1016/j.na.2016.06.003

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