Math. Model. Nat. Phenom.
Volume 3, Number 7, 2008Special issue dedicated to Glenn Webb
|Page(s)||49 - 77|
|Published online||23 October 2008|
An Age and Spatially Structured Population Model for Proteus Mirabilis Swarm-Colony Development
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
Corresponding author: email@example.com
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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