Asymptotic behavior of a singular transport equation modelling cell division

Pages: 439 - 456, Volume 3, Issue 3, August 2003

doi:10.3934/dcdsb.2003.3.439       Abstract        Full Text (169.1K)       Related Articles

Mostafa Adimy - Laboratoire de Mathématiques Appliquées, FRE 2570, Université de Pau et des Pays de l'Adour, Avenue de l'université, 64000 Pau, France (email)
Laurent Pujo-Menjouet - Department of Physiology, McGill University, McIntyre Medical Sciences Building, 3655 Promenade Sir William Osler, Montreal, QC, Canada H3G 1Y6, Canada (email)

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.

Received: May 2002;      Revised: January 2003;      Published: May 2003.