A Hydrodynamic Limit for Chemotaxis in a Given Heterogeneous Environment
Stefan Grosskinsky, Daniel Marahrens, and Angela Stevens
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Submission date: 14. Aug. 2015
published in: Vietnam journal of mathematics, 45 (2017) 1-2, p. 127-152
DOI number (of the published article): 10.1007/s10013-016-0209-8
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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  and Kipnis/Landim . Numerical simulations extend and illustrate the theoretical findings.