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

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dc.creatorHilhorst, Danielle
dc.creatorKing, John R.
dc.creatorRöger, Matthias
dc.date2007-02-28
dc.date.accessioned2026-07-07T07:49:40Z
dc.date.available2026-07-07T07:49:40Z
dc.descriptionWe 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, nonlinear selection of the minimal speed occurs.
dc.description15 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/math/0702886
dc.identifierhttp://arxiv.org/abs/math/0702886
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/124942
dc.subjectAnalysis of PDEs
dc.subjectTissues and Organs
dc.subject35K57; 92E20; 35B25; 80A22
dc.titleTravelling-wave analysis of a model describing tissue degradation by bacteria
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