Dr. M. Roeger (TU Eindhoven)
Mathematical analysis of a model describing tissue degradation by bacteria
(Joint work with D. Hilhorst, Paris-Sud, and J. R. King, Nottingham)
A basic model for the penetration of healthy tissue by bacteria is
presented. There, the bacteria produce enzymes which react with and
destroy the tissue, providing space and nutrients for the bacteria. The
model problem is given by a coupled system of a parabolic and an ordinary
differential equation and a typically large parameter governs the
degradation rate. As this parameter tends to infinity a Stefan-like limit
problem is obtained.
In this talk we focus on the analysis of travelling wave solutions.
Existence of travelling waves can be shown for a continuum of speeds and
one crucial question is the identification of the minimal speed. Depending
on the value of the degradation parameter we find two different
principles which determine the minimal speed.