Asymptotic behavior of a singular transport equation modelling cell division

Discrete and Continuous Dynamical Systems - Series B

Volumn 3, Issue 3, 2003, Pages 439-456

  Adimy, Mostafa ^a   Pujo Menjouet, Laurent ^b  

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

^b MCGILL UNIVERSITY   (Canada)

Author keywords

Structured Population, Cell cycle, First order partial differential equation with delays, Stem Cells, Delay, Aplastic Anemia, Instability

Indexed keywords

EID: 0043037214     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2003.3.439     Document Type: Article

References (19)

1. M. Adimy and L. Pujo-Menjouet, A SINGULAR TRANSPORT MODEL DESCRIBING CELLULAR DIVISION, C. R. Acad. Sci. Paris, t. 332, Série I, (2001), 1071-1076.
2. S. Bernard, J. Bélair and M.C. Mackey, SUFFICIENT CONDITIONS FOR STABILITY OF LINEAR DIFFERENTIAL EQUATIONS WITH DISTRIBUTED DELAY, Cont. and Disc. Dynam. Syst. Ser. B, 1, No.2, (2001), 233-256.
3. R. Crabb, M.C. Mackey and A. Rey, PROPAGATING FRONTS, CHAOS AND MULTISTABILITY IN A CELL REPLICATION MODEL, Chaos, 3, (1996), 477-492.
4. J. Dyson, R. Villella-Bressan and G.F. Webb, A SINGULAR TRANSPORT EQUATION MODELLING A PROLIFERATING MATURITY STRUCTURED CELL POPULATION, Can. Appl. Math. Quart., 4, (1996a), 65-95.
5. J. Dyson, R. Villella-Bressan and G.F. Webb, A SINGULAR TRANSPORT EQUATION WITH DELAYS, Second International Conference on Differential Equations in Marrakesh, (1996b).
6. J. Dyson, R. Villella-Bressan and G.F. Webb, A NONLINEAR AGE AND MATURITY STRUCTURED MODEL OF POPULATION DYNAMICS. I. BASIC THEORY, J. Math. Anal. Appl., 242, (2000a), 93-104.
7. J. Dyson, R. Villella-Bressan and G.F. Webb, A NONLINEAR AGE AND MATURITY STRUCTURED MODEL OF POPULATION DYNAMICS. II. CHAOS, J. Math. Anal. Appl., 242, (2000b), 255-270.
8. M. Gyllenberg and H.J.A.M. Heijmans, AN ABSTRACT DELAY-DIFFERENTIAL EQUATION MODELLING SIZE DEPENDENT CELL GROWTH AND DIVISION, SIAM J. Math. Anal., 18, (1987), 74-88.
9. M.C. Mackey, UNIFIED HYPOTHESIS OF THE ORIGIN OF APLASTIC ANEMIA AND PERIODIC HEMATOPOIESIS, Blood, 51, (1978), 941-956.
10. M. C. Mackey, DYNAMIC HEMATOLOGICAL DISORDERS OF STEM CELL ORIGIN, BIOPHYSICAL AND BIOCHEMICAL INFORMATION TRANSFER IN RECOGNITION, 373-409, Eds. Vassileva-Popova J. G., Jensen E. V. New-york: Plenum Press, 1979.
11. M.C. Mackey and P. Dörmer, CONTINUOUS MATURATION OF PROLIFERATING ERYTHROID PRECURSORS, Cell Tissue Kinet., 15, (1982), 381-392.
12. M.C. Mackey and R. Rudnicki, GLOBAL STABILITY IN A DELAYED PARTIAL DIFFERENTIAL EQUATION DESCRIBING CELLULAR REPLICATION, J. Math. Biol., 33, (1994), 89-109.
13. M.C. Mackey and R. Rudnicki, A NEW CRITERION FOR THE GLOBAL STABILITY OF SIMULTANEOUS CELL REPLICATION AND MATURATION PROCESSES, J. Math. Biol., 38, (1999), 195-219.
14. J.A.J. Metz and O. Diekmann, THE DYNAMICS OF PHYSIOLOGICALLY STRUCTURED POPULATIONS, Lecture Notes in Biomathematics, 68, Springer-Verlag, 1986.
15. L. Pujo-Menjouet and R. Rudnicki, GLOBAL STABILITY OF CELLULAR POPULATIONS WITH UNEQUAL DIVISION, Can. Applied Math. Quart., Vol.8, No.2, (2000), 185-203.
16. A. Rey and M.C. Mackey, BIFURCATIONS AND TRAVELING WAVES IN A DELAYED PARTIAL DIFFERENTIAL EQUATION, Chaos, 2 , (1992), 231-244.
17. A. Rey and M.C. Mackey, MULTISTABILITY AND BOUNDARY LAYER DEVELOPMENT IN A TRANSPORT EQUATION WITH RETARDED ARGUMENTS, Can. Appl. Math. Quart., 1, (1993), 61-81.
18. A. Rey and M.C. Mackey, TRANSITIONS AND KINEMATICS OF REACTION-CONVECTION FRONTS IN A CELL POPULATION MODEL, Physica D, 80, (1995a), 120-139.
19. A. Rey and M.C. Mackey, PROPAGATION OF POPULATION PULSES AND FRONTS IN A CELL REPLICATION PROBLEM: NON-LOCALITY AND DEPENDENCE ON THE INITIAL FUNCTION, Physica D, 86, (1995b), 373-395.