Stochastic homogenization of the Keller-Segel chemotaxis system

14 Sep 2016  ·  Matzavinos Anastasios, Ptashnyk Mariya ·

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. read more

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Analysis of PDEs Probability Quantitative Methods