  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.
