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Stochastic particle models and chemotactic/haptotactic motion of cells

Presented by: 
Angela Stevens Westfalische Wilhelms-Universitat Munster
Date: 
Wednesday 9th December 2015 - 11:30 to 12:30
Venue: 
INI Seminar Room 1
Abstract: 
Co-authors: Stefan Grosskinsky (University of Warwick), Daniel Marahrens (formerly MPI MIS Leipzig), Juan Velazquez (University of Bonn)

In this talk 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. They interact directly among themselves only 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 Koukkous and Kipnis/Landim. Further PDE-ODE based haptotaxis models are discussed and their relation to attractive reinforced random walks.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons