Geodesic
An Age and Spatially Structured Population Model for Proteus Mirabilis Swarm-Colony Development
Ph. Laurençot1 ; 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
Mathematical modelling of natural phenomena, Tome 3 (2008) no. 7, pp. 49-77

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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.
DOI : 10.1051/mmnp:2008041

Ph. Laurençot 1 ; Ch. Walker 2

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 
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Ph. Laurençot; Ch. Walker. An Age and Spatially Structured Population Model for Proteus Mirabilis Swarm-Colony Development. Mathematical modelling of natural phenomena, Tome 3 (2008) no. 7, pp. 49-77. doi: 10.1051/mmnp:2008041

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