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.