Global stability of a partial differential equation with distributed delay due to cellular replication

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 nonlinear partial differential equation, arising from a model of cellular proliferation. This model describes the production of blood cells in the bone marrow. It is represented by a partial differential equation with a retardation of the maturation variable and a distributed temporal delay. Our aim is to prove that the behaviour of primitive cells influences the global behaviour of the population.

Mots clés: hematopoiesis modelling; hyperbolic partial differential equations; global asymptotic stability; distributed delay

Domaines: Equations aux dérivées partielles [math.AP]

Mostafa Adimy, Fabien Crauste. Global stability of a partial differential equation with distributed delay due to cellular replication. Nonlinear Analysis: Theory, Methods and Applications, 2003, 54 (8), pp.1469-1491. ⟨10.1016/S0362-546X(03)00197-4⟩. ⟨hal-00375926⟩