Asymptotic behavior of a singular transport equation modelling cell division

Mostafa Adimy; Laurent Pujo-Menjouet

doi:10.3934/dcdsb.2003.3.439

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2003, Volume 3, Issue 3: 439-456. Doi: 10.3934/dcdsb.2003.3.439

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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
2.
Department of Physiology, McGill University, McIntyre Medical Sciences Building, 3655 Promenade Sir William Osler, Montreal, QC, Canada H3G 1Y6

Received: April 30, 2002

Revised: December 31, 2002

Published: July 2003

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Abstract

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:

Structured population,
cell cycle,
first order partial differential equation with delays,
stem cells,
delay,
aplastic anemia,
instability.

Mathematics Subject Classification: 35F15, 35L60, 92C37, 92D25.

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