A Mathematical Study in the Theory of Dynamic Population

This article deals with a mathematical model of an age structured proliferating cell population originally proposed by Lebowitz and Rubinow J. Math. Biol. 1 Ž1974., 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.