Un modèle non-linéaire de prolifération cellulaire : extinction des cellules et invariance

Mostafa Adimy (1, 2) , Fabien Crauste (3)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 ANUBIS - Tools of automatic control for scientific computing, Models and Methods in Biomathematics
3 LMAP - Laboratoire de Mathématiques appliquées de Pau

This paper analyses a nonlinear age-maturity structured system which arises as a model of the blood cellular production in the bone marrow. The resulting model is a nonlinear first-order partial differential equation in which there is a distributed temporal delay and a retardation in the maturation variable. We prove that uniqueness of solutions depends only on small maturity cells (stem cells) and we give a result of invariance.

Mots clés: Age-structured system; transport equations; distributed delay : nonlocal model

Domaines: Equations aux dérivées partielles [math.AP]

Mostafa Adimy, Fabien Crauste. Un modèle non-linéaire de prolifération cellulaire : extinction des cellules et invariance. Comptes Rendus. Mathématique, 2003, 336 (7), pp.559-564. ⟨10.1016/S1631-073X(03)00125-0⟩. ⟨hal-00375916⟩