| Issue |
Math. Model. Nat. Phenom.
Volume 3, Number 7, 2008
Special issue dedicated to Glenn Webb
|
|
|---|---|---|
| Page(s) | 49 - 77 | |
| DOI | https://doi.org/10.1051/mmnp:2008041 | |
| Published online | 23 October 2008 | |
An Age and Spatially Structured Population Model for Proteus Mirabilis Swarm-Colony Development
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
Corresponding author: walker@ifam.uni-hannover.de
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.