Details
| Original language | English |
|---|---|
| Pages (from-to) | 49-77 |
| Number of pages | 29 |
| Journal | Mathematical Modelling of Natural Phenomena |
| Volume | 3 |
| Issue number | 7 |
| Publication status | Published - Jan 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.
Keywords
- age structure, degenerate diffusion, population models
ASJC Scopus subject areas
- Mathematics(all)
- Modelling and Simulation
- Mathematics(all)
- Applied Mathematics
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In: Mathematical Modelling of Natural Phenomena, Vol. 3, No. 7, 01.2008, p. 49-77.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - An age and spatially structured population model for proteus mirabilis swarm-colony development
AU - Laurençot, Ph
AU - Walker, Ch
N1 - Copyright: Copyright 2011 Elsevier B.V., All rights reserved.
PY - 2008/1
Y1 - 2008/1
N2 - 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.
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.
KW - age structure
KW - degenerate diffusion
KW - population models
UR - http://www.scopus.com/inward/record.url?scp=71549142665&partnerID=8YFLogxK
U2 - 10.1051/mmnp:2008041
DO - 10.1051/mmnp:2008041
M3 - Article
AN - SCOPUS:71549142665
VL - 3
SP - 49
EP - 77
JO - Mathematical Modelling of Natural Phenomena
JF - Mathematical Modelling of Natural Phenomena
SN - 0973-5348
IS - 7
ER -