Talk abstract:

Moment Closure of Reaction Transport Equations

Thomas Hillen
University of Utah
hillen@math.utah.edu

Reaction transport equations are models for spatial spread and interactions of particles which base on the individual behavior of the underlying species. Relevant parameters (e.g. mean run length, turnangle distribution, etc.) can be measured in experiments. The full kinetic transport problem is hard to handle both analytically and numerically. Hence we consider reductions which cover basic properties. In this talk I derive equations for the velocity moments and I present a general procedure to close the moment system on each level. The two moment approximation is a Cattaneo system, which is closely related to a damped wave equation. The relevant parameters are directly related to biological observables. In case of chemotaxis a chemotaxis-Cattaneo model results, which in the parabolic limit converges to the well known Keller-Segel equations.

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1998-1999 Mathematics in Biology