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MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
46/2015

A Hydrodynamic Limit for Chemotaxis in a Given Heterogeneous Environment

Stefan Grosskinsky, Daniel Marahrens and Angela Stevens

Abstract

In this paper the first equation within a class of well known chemotaxis systems is derived as a hydrodynamic limit from a stochastic interacting many particle system on the lattice. The cells are assumed to interact with attractive chemical molecules on a finite number of lattice sites, but they only directly interact among themselves on the same lattice site. The chemical environment is assumed to be stationary with a slowly varying mean, which results in a non-trivial macroscopic chemotaxis equation for the cells. Methodologically the limiting procedure and its proofs are based on results by Koukkus [18] and Kipnis/Landim [17]. Numerical simulations extend and illustrate the theoretical findings.

Received:
Aug 14, 2015
Published:
Aug 20, 2015

Related publications

inJournal
2017 Repository Open Access
Stefan Grosskinsky, Daniel Marahrens and Angela Stevens

A hydrodynamic limit for chemotaxis in a given heterogeneous environment

In: Vietnam journal of mathematics, 45 (2017) 1-2, pp. 127-152