A Mathematical Study for a Rotenberg Model

This paper deals with a mathematical model in cell dynamics population originally proposed by M.R otenberg (1983, J. Theoret. Biol. 103, 181–199).Individual cells are distinguished by their degree of maturity and maturation velocity.Here, all biological rules are considered.W e bring new techniques to the discussion of this model. We show that the model is well posed in the sense of the theory of semigroups, we study the positivity and irreducibility of the generated semigroups, and we calculate its essential type.The asymptotic behavior is obtained in uniform topology.