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Issue Math. Model. Nat. Phenom.
Volume 3, Number 7, 2008
Special issue dedicated to Glenn Webb
Page(s) 49 - 77
DOI 10.1051/mmnp:2008041
Published online 23 October 2008

Math. Model. Nat. Phenom. Vol. 3, No. 7, 2008, pp. 49-77
DOI: 10.1051/mmnp:2008041

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

Ph. Laurençot1 and Ch. Walker2

1  Institut de Mathématiques de Toulouse, CNRS (UMR 5219) & Université de Toulouse, 118 route de Narbonne, F-31062 Toulouse cedex 9, France
2  Leibniz Universität Hannover, Institut für Angewandte Mathematik, Welfengarten 1, D-30167 Hannover, Germany

walker@ifam.uni-hannover.de

Published online: 23 October 2008

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.


Mathematics Subject Classification. 92C17, 35G25, 35M20, 35K65, 47N20

Key words: population models -- age structure -- degenerate diffusion





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