MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

MiS Preprint

A Hydrodynamic Limit for Chemotaxis in a Given Heterogeneous Environment

Stefan Grosskinsky, Daniel Marahrens and Angela Stevens


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.

Aug 14, 2015
Aug 20, 2015

Related publications

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