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

Nonlinear Analysis, Theory, Methods and Applications

Volumn 54, Issue 8, 2003, Pages 1469-1491

  Adimy, Mostafa ^a   Crauste, Fabien ^a  

^a UNIVERSITÉ DE PAU ET DES PAYS DE L'ADOUR   (France)

Author keywords

Age maturity structured model; Blood production system; Cell replication; Distributed delay; Local and global stability; Nonlinear partial differential equation

Indexed keywords

BLOOD; BONE; CELLS;

CELLULAR REPLICATION;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0041627599     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(03)00197-4     Document Type: Article

References (16)

1. Adimy M., Pujo-Menjouet L. A singular transport model describing cellular division. C. R. Acad. Sci. Paris Ser. I, Math. 332(12):2001;1071-1076.
2. M. Adimy, L. Pujo-Menjouet, Asymptotic behaviour of a singular transport equation modelling cell division, Discrete Continuous Dyn. System Ser. B, 3 (2003) 439-456.
3. Bradford G., Williams B., Rossi R., Bertoncello I. Quiescence, cycling, and turnover in the primitive haematopoietic stem cell compartment. Exp. Hematol. 25:1997;445-453.
4. 0 phase in the cell cycle Cell. Tissue Kinet. 19:1970;321-334.
5. R. Crabb, J. Losson, M.C. Mackey, Dependence on initial conditions in non local PDE's and heredetary dynamical systems, Proceedings of the International Conference on Nonlinear Analysis, Vol. 4, Tampa Bay, de Gruyter, Berlin, 1996, pp. 3125-3136.
6. Crabb R., Mackey M.C., Rey A. Propagating fronts, chaos and multistability in a cell replication model. Chaos. 6:1996;477-492.
7. Dyson J., Villella-Bressan R., Webb G.F. A singular transport equation modelling a proliferating maturity structured cell population. Can. Appl. Math. Q. 4:1996;65-95.
8. Dyson J., Villella-Bressan R., Webb G.F. A nonlinear age and maturity structured model of population dynamics. I. basic theory J. Math. Anal. Appl. 242(1):2000;93-104.
9. Dyson J., Villella-Bressan R., Webb G.F. A nonlinear age and maturity structured model of population dynamics. II. chaos J. Math. Anal. Appl. 242(2):2000;255-270.
10. J. Hale, S.M. Verduyn Lunel, Introduction to Functional Differential Equations, Applied Mathematical Sciences, Vol. 99, Springer, New York, 1993, 447pp.
11. Mackey M.C. Unified hypothesis of the origin of aplastic anaemia and periodic hematopoiesis. Blood. 51:1978;941-956.
12. Mackey M.C., Rey A. Multistability and boundary layer development in a transport equation with retarded arguments. Can. Appl. Math. Quart. 1:1993;1-21.
13. Mackey M.C., Rey A. Transitions and kinematics of reaction-convection fronts in a cell population model. Physica D. 80:1995;120-139.
14. Mackey M.C., Rey A. Propagation of population pulses and fronts in a cell replication problem. non-locality and dependence on the initial function Physica D. 86:1995;373-395.
15. Mackey M.C., Rudnicki R. Global stability in a delayed partial differential equation describing cellular replication. J. Math. Biol. 33:1994;89-109.
16. Mackey M.C., Rudnicki R. A new criterion for the global stability of simultaneous cell replication and maturation processes. J. Math. Biol. 38:1999;195-219.