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

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.