Study of a Lebowitz-Rubinow's model

In this Note the Lebowirz-Rubinow's model describing the evolution of a cel l population is discussed In this model, a cell is distinguished by its age and its cell cycle length. We show the existence of a generated semigroup and we study its positivity and its irreducibility. We prove the eventually compactness of the generated semigroup and its convergence to one rank pi- ejection in the operators norm topology. (C) 1999 Academie des Sciences/Edi tions scientifiques et medicales Elsevier SAS.