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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
*
walker@ifam.uni-hannover.de
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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 been shown to display these structures when solved numerically. The model consists of an ordinary differential equation coupled with a partial differential equation involving a first-order hyperbolic aging term together with nonlinear degenerate diffusion. The system is shown to admit 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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