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MiS Preprint

Travelling-wave analysis of a model describing tissue degradation by bacteria

Danielle Hilhorst, John R. King and Matthias Röger


We study travelling-wave solutions for a reaction-diffusion system arising as a model for host-tissue degradation by bacteria. This system consists of a parabolic equation coupled with an ordinary differential equation. For large values of the 'degradation-rate parameter' solutions are well approximated by solutions of a Stefan-like free boundary problem, for which travelling-wave solutions can be found explicitly. Our aim is to prove the existence of travelling waves for all sufficiently large wave-speeds for the original reaction-diffusion system and to determine the minimal speed. We prove that for all sufficiently large degradation rates the minimal speed is identical to the minimal speed of the limit problem. In particular, in this parameter range, shape nonlinear selection of the minimal speed occurs.

Feb 28, 2007
Feb 28, 2007
MSC Codes:
35K57, 92E20, 35B25, 80A22
Travelling waves, reaction-diffusion system, Stefan problem

Related publications

2007 Repository Open Access
D. Hilhorst, J. R. King and Matthias Röger

Travelling-wave analysis of a model describing tissue degradation by bacteria

In: European journal of applied mathematics, 18 (2007) 5, pp. 583-605