No abstract

This article deals with a mathematical model of an age structured proliferating w cell population originally proposed by Lebowitz and Rubinow J. Math. Biol. 1 Ž . x 1974 , 17᎐36 . Individual cells are distinguished by age and by cell cycle length. The cell cycle length is considered as an inherited property determined at birth. Here, general boundary conditions are considered by means of a linear and bounded operator K. After establishing the theorem of traces, we show that the model is well posed in the sense of the theory of semigroup without restriction on the boundary operator K. We study the positivity and the irreducibility of the generated semigroup and we calculate its essential type. The asymptotic behavior is obtained in the uniform topology. ᮊ

This work deals with a mathematical model of an age‐cycle length structured cell population. Each cell is distinguished by its age and its cycle length. The cellular mitosis is mathematically described by non‐compact boundary conditions. We prove then that this mathematical model is governed by a positive C0‐semigroup. Copyright © 2014 John Wiley & Sons, Ltd.