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

被引：6

作者：

Laurencot, Ph. ^{[2
,3
]}

Walker, Ch. ^{[1
]}

机构：

[1] Leibniz Univ Hannover, Inst Angew Math, D-30167 Hannover, Germany

[2] CNRS, UMR 5219, Inst Math Toulouse, F-31062 Toulouse 9, France

[3] Univ Toulouse, F-31062 Toulouse 9, France

来源：

MATHEMATICAL MODELLING OF NATURAL PHENOMENA | 2008年 / 3卷 / 07期

关键词：

population models; age structure; degenerate diffusion;

D O I：

10.1051/mmnp:2008041

中图分类号：

Q [生物科学];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

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.

引用

页码：49 / 77

页数：29

共 19 条

[1] DUAL SEMIGROUPS AND 2ND ORDER LINEAR ELLIPTIC BOUNDARY-VALUE-PROBLEMS [J].

AMANN, H .

ISRAEL JOURNAL OF MATHEMATICS, 1983, 45 (2-3) :225-254

[2] DYNAMIC THEORY OF QUASILINEAR PARABOLIC-SYSTEMS .3. GLOBAL EXISTENCE [J].

AMANN, H .

MATHEMATISCHE ZEITSCHRIFT, 1989, 202 (02) :219-250

[3]

Amann H., 1995, Abstract Linear Theory, Monographs inMathematics, V89, DOI DOI 10.1007/978-3-0348-9221-6

[4] Global existence for a degenerate nonlinear diffusion problem with nonlinear gradient term and source [J].

Andreu, F ;

Mazón, JM ;

Simondon, F ;

Toledo, J .

MATHEMATISCHE ANNALEN, 1999, 314 (04) :703-728

[5] A structured-population model of Proteus mirabilis swarm-colony development [J].

Ayati, BP .

JOURNAL OF MATHEMATICAL BIOLOGY, 2006, 52 (01) :93-114

[6] Modeling the role of the cell cycle in regulating Proteus mirabilis swarm-colony development [J].

Ayati, Bruce P. .

APPLIED MATHEMATICS LETTERS, 2007, 20 (08) :913-918

[7]

CZIROK A, 2001, PHYS REV E, V36

[8] Kinetic model of Proteus mirabilis swarm colony development [J].

Esipov, SE ;

Shapiro, JA .

JOURNAL OF MATHEMATICAL BIOLOGY, 1998, 36 (03) :249-268

[9]

Frénod E, 2006, DIFFER INTEGRAL EQU, V19, P697

[10]

LAURENCOT P, PROTEUS MIRABI UNPUB

← 1 2 →