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An Age and Spatially Structured Population Modelfor Proteus Mirabilis Swarm-Colony Development

Published online by Cambridge University Press:  23 October 2008

Ph. Laurençot  and
Ch. Walker
Ph. Laurençot
Affiliation:
Institut de Mathématiques de Toulouse, CNRS (UMR 5219) & Université de Toulouse, 118 route de Narbonne, F-31062 Toulouse cedex 9, France
Ch. Walker*
Affiliation:
Leibniz Universität Hannover, Institut für Angewandte Mathematik, Welfengarten 1, D-30167 Hannover, Germany
*
[email protected]
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Abstract

Proteus mirabilis are bacteria that make strikingly regular spatial-temporal patterns on agar surfaces.In this paper we investigate a mathematical model that has beenshown to display these structures when solved numerically. The model consists of an ordinarydifferential equation coupled with a partial differential equation involving a first-orderhyperbolic aging term together with nonlinear degenerate diffusion. The system is shown toadmit global weak solutions.

Keywords

population modelsage structuredegenerate diffusion
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 3 , Issue 7: Special issue dedicated to Glenn Webb , 2008 , pp. 49 - 77
Copyright
© EDP Sciences, 2008

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