A mathematical study in the theory of dynamic population

This article deals with a mathematical model of an age structured prolifera ting cell population originally proposed by Lebowitz and Rubinow [J. Math. Biol. 1 (1974), 17-36]. Individual cells are distinguished by age and by ce ll cycle length. The cell cycle length is considered as an inherited proper ty determined at birth. Here, general boundary conditions are considered by means of a linear and bounded operator K. After establishing the theorem o f traces, we show that the model is well posed in the sense of the theory o f semigroup without restriction on the boundary operator K. We study the po sitivity and the irreducibility of the generated semigroup and we calculate its essential type. The asymptotic behavior is obtained in the uniform top ology, (C) 2001 Academic Press.