Global stability of a partial differential equation with distributed delay due to cellular replication

被引：68

作者：

Adimy, M ^{[1
]}

Crauste, F ^{[1
]}

机构：

[1] Univ Pau & Pays Adour, Dept Math Appl, F-64000 Pau, France

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2003年 / 54卷 / 08期

关键词：

local and global stability; nonlinear partial differential equation; distributed delay; age-maturity structured model; blood production system; cell replication;

D O I：

10.1016/S0362-546X(03)00197-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 [应用数学];

摘要：

In this paper, we investigate a nonlinear partial differential equation, arising from a model of cellular proliferation. This model describes the production of blood cells in the bone marrow. It is represented by a partial differential equation with a retardation of the maturation variable and a distributed temporal delay. Our aim is to prove that the behaviour of primitive cells influences the global behaviour of the population. (C) 2003 Elsevier Ltd. All rights reserved.

引用

页码：1469 / 1491

页数：23

共 16 条

[1]

Adimy M, 2003, DISCRETE CONT DYN-B, V3, P439

[2]

A singular transport model describing cellular division [J].

Adimy, M ;

Pujo-Menjouet, L .

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 2001, 332 (12) :1071-1076

[3]

[Anonymous], PARASITES PATHOGENS

[4]

Bradford GB, 1997, EXP HEMATOL, V25, P445

[5]

ON EXISTENCE OF A G0-PHASE IN CELL CYCLE [J].

BURNS, FJ ;

TANNOCK, IF .

CELL AND TISSUE KINETICS, 1970, 3 (04) :321-&

[6]

Propagating fronts, chaos and multistability in a cell replication model [J].

Crabb, R ;

Mackey, MC ;

Rey, AD .

CHAOS, 1996, 6 (03) :477-492

[7]

CRABB R, 1996, P INT C NONL AN TAMP, V4, P3125

[8]

A nonlinear age and maturity structured model of population dynamics - II. Chaos [J].

Dyson, J ;

Villella-Bressan, R ;

Webb, G .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2000, 242 (02) :255-270

[9]

A nonlinear age and maturity structured model of population dynamics - I. Basic theory [J].

Dyson, J ;

Villea-Bressan, R ;

Webb, G .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2000, 242 (01) :93-104

[10]

Dyson J., 1996, CAN APPL MATH Q, V4, P65

← 1 2 →