Danielle Hilhorst Université de ParisSud (France)
A reactiondiffusion 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 reactiondiffusion equations, together with
homogeneous Neumann boundary conditions and initial conditions. The unknown functions u_{k} and w_{k} are such
that u_{k} corresponds to the concentration of degradative enzymes produced by the bacteria, and 1  w_{k}
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
(u_{k},w_{k}) 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.
