Danielle Hilhorst

Université de Paris-Sud (France)

A reaction-diffusion system descriging tissue degradation by bacteria

We consider a model for the penetration of healthy tissue by bacteria from a burn wound. The mathematical formulation is given by a coupled system of two parabolic reaction-diffusion equations, together with homogeneous Neumann boundary conditions and initial conditions. The unknown functions uk and wk are such that uk corresponds to the concentration of degradative enzymes produced by the bacteria, and 1 - wk corresponds to the volume fraction of healthy tissue. The key parameter k > 0 is typically very large and governs the degradation of ratio of the tissue. We describe the singular limit of the solution (uk,wk) as k tends to infinity and characterise the limit function pair (u,w) in terms of the weak solution of an auxiliary problem. Further results deal with the fast degradation rate limit of corresponding travelling wave solutions. This is joint work with John King and Matthias Röger.