A Model of Proliferating Cell Populations with Infinite Cell Cycle Length: Semigroup Existence

In this paper we are concerned with a mathematical model of an age structured cell population endowed with general reproduction laws. Individual cells are distinguished by age and cell cycle length. The cell cycle length is considered as an inherited property determined at birth and can be between zero and infinity. We show that the model is well-posed in the sense of the semigroup theory and we give its explicit expression.