Abstract :
In this paper we complete the study of Rotenberg’s model M. Rotenberg, 1983,
J. Theoret. Biol. 103, 181]199. describing the growth of a cell population and
treated partially by M. Boulanouar and H. Emamirad Differential Integral Equa-
tions, 13 2000., 125]144.. In contrast to our previously cited treatment, here we
impose the condition that the maturation velocity for any cell can become null.
This consideration implies that the cell population never completely leaves its
initial distribution, because at every time we can find some cells of initial cell
population that are not divided. In this case, the generated semigroup is not
compact. To surmount this difficulty, after studying the irreducibility of the
generated semigroup, we calculate explicitly its essential type and we show the
asymptotic convergence of the generated semigroup to a projection of rank 1.
