Mathematical study of a Rotenberg model

In this paper, a cell proliferation model of Rotenberg is mathematically st udied. Each cell of this population is distinguished by its degree of matur ity mu and its maturation velocity v. We equipped this mathematical model b y boundary conditions wich generalize all biological rules imposed by Roten berg. We show that this model is governed by a strongly continuous semigrou p. We also develop some properties of this semigroup and we study its asymp totic behaviour in the uniform topology. (C) 2000 Editions scientifiques et medicales Elsevier SAS.