Asymptotic behavior of a singular transport equation modelling cell division
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)
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.
Received: May 2002; Revised: January 2003; Published: May 2003.
2011 Impact Factor.921