Existence, positivity and stability for a nonlinear model of cellular proliferation

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

In this paper, we investigate a system of two nonlinear partial differential equations, arising from a model of cellular proliferation which describes the production of blood cells in the bone marrow. Due to cellular replication, the two partial differential equations exhibit a retardation of the maturation variable and a temporal delay depending on this maturity. We show that this model has a unique solution which is global under a classical Lipschitz condition. We also obtain the positivity of the solutions and the local and global stability of the trivial equilibrium.

Mots clés: nonlinear partial differential equation; age-maturity structured model; blood production system; delay depending on the maturity; positivity; local and global stability

Domaines: Equations aux dérivées partielles [math.AP]

Mostafa Adimy, Fabien Crauste. Existence, positivity and stability for a nonlinear model of cellular proliferation. Nonlinear Analysis: Real World Applications, 2005, 6 (2), pp.337-366. ⟨10.1016/j.nonrwa.2004.09.001⟩. ⟨hal-00375934⟩