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August  2003, 3(3): 439-456. doi: 10.3934/dcdsb.2003.3.439

Asymptotic behavior of a singular transport equation modelling cell division

Mostafa Adimy 1, and  Laurent Pujo-Menjouet 2,

1. 

Laboratoire de Mathématiques Appliquées, FRE 2570, Université de Pau et des Pays de l'Adour, Avenue de l'université, 64000 Pau, France
2. 

Department of Physiology, McGill University, McIntyre Medical Sciences Building, 3655 Promenade Sir William Osler, Montreal, QC, Canada H3G 1Y6, Canada

Received  May 2002 Revised  January 2003 Published  May 2003

This paper analyses the behavior of the solutions of a model of cells that are capable of simultaneous proliferation and maturation. This model is described by a first-order singular partial differential system with a retardation of the maturation variable and a time delay. Both delays are due to cell replication. We prove that uniqueness and asymptotic behavior of solutions depend only on cells with small maturity (stem cells).
Keywords: delay, instability., Structured population, stem cells, cell cycle, first order partial differential equation with delays, aplastic anemia.
Mathematics Subject Classification: 35F15, 35L60, 92C37, 92D2.
Citation: Mostafa Adimy, Laurent Pujo-Menjouet. Asymptotic behavior of a singular transport equation modelling cell division. Discrete & Continuous Dynamical Systems - B, 2003, 3 (3) : 439-456. doi: 10.3934/dcdsb.2003.3.439
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