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

Ph. Laurençot; Ch. Walker

Mathematical Modelling of Natural Phenomena (2008)

  • Volume: 3, Issue: 7, page 49-77
  • ISSN: 0973-5348

Abstract

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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.

How to cite

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Laurençot, Ph., and Walker, Ch.. "An Age and Spatially Structured Population Model for Proteus Mirabilis Swarm-Colony Development." Mathematical Modelling of Natural Phenomena 3.7 (2008): 49-77. <http://eudml.org/doc/222328>.

@article{Laurençot2008,
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. },
author = {Laurençot, Ph., Walker, Ch.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {population models; age structure; degenerate diffusion},
language = {eng},
month = {10},
number = {7},
pages = {49-77},
publisher = {EDP Sciences},
title = {An Age and Spatially Structured Population Model for Proteus Mirabilis Swarm-Colony Development},
url = {http://eudml.org/doc/222328},
volume = {3},
year = {2008},
}

TY - JOUR
AU - Laurençot, Ph.
AU - Walker, Ch.
TI - An Age and Spatially Structured Population Model for Proteus Mirabilis Swarm-Colony Development
JO - Mathematical Modelling of Natural Phenomena
DA - 2008/10//
PB - EDP Sciences
VL - 3
IS - 7
SP - 49
EP - 77
AB - 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.
LA - eng
KW - population models; age structure; degenerate diffusion
UR - http://eudml.org/doc/222328
ER -

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