F Oct. 22

Wenzhang Huang, Department of Mathematical Sciences, University of Alabama
at Huntsville

Title: Traveling wave solutions for a biological reaction-diffusion
model.

Abstract: We investigate the existence of traveling wave solutions for
a system of reaction-diffusion equations that has been used as a model
for the microbial growth and competition in a flow reactor as well as
for the diffusive epidemic population. For a single species model, the
existence of traveling waves was conjectured early and has been
proved recently for sufficiently small diffusion coefficient by a
singular perturbation technique.  In this talk, we first use the
shooting method to show the existence and uniqueness of traveling
waves for a single species model  with  arbitrary diffusion coefficients.
We then use a continuity argument and the results for the single
model to prove the existence of traveling wave solutions for the
model with two competing species.