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. Walker<sup>2

1</sup>  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

What is OpenURL?