Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
839172 | Nonlinear Analysis: Theory, Methods & Applications | 2016 | 19 Pages |
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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Authors
Anastasios Matzavinos, Mariya Ptashnyk,