Reductions of Reaction-Transport-Equations

                                   by

                              Dr. Thomas Hillen
               Department of Mathematics, University of Utah

               INSCC 110, 3:30pm  Monday, March 22, 1999


                                Abstract

                           
In this talk I consider nonlinear transport equations which are
relevant as models for biological populations. The full kinetic transport
model is hard to analyze analytically and numerically. Hence one is forced
to consider caricatures of the full model, which cover the right 
dynamic behavior. Two approaches are presented here:

1. From the transport equation one can derive a (infinite)
sequence of hyperbolic subsystems for the velocity moments. Here I present an
energy method to close the first two moment equations (Cattaneo
approximation).

2. In a limit of high speed and small mean free path length the
transport model behaves like a diffusion process (parabolic limit). I will
give higher order approximations, based on this scaling property, and
I will discuss Hilbert's paradox. (This part is joint work with H.
Othmer).

A study of error estimates shows that the Cattaneo approximation 
is accurate for all times on large space scales, whereas the
parabolic limit describes the long time asymptotics of the transport
problem. 

Request for preprints and reprints to Thomas Hillen <hillen@math.utah.edu>
This information can be found at http://www.math.utah.edu/research/