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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  and Kipnis/Landim . Numerical simulations extend and illustrate the theoretical findings.