A model of proliferating cell populations with inherited cycle length (Q1079142)

In the \textit{J. L. Lebowitz} and \textit{S. J. Rubinow} model [ibid. 1, 17-36 (1974)] a cell population is described through a density function which depends on the age, the time and the cell cycle length, which is a hereditable and unchanging property of individual cells. In this paper this model is mathematically elaborated under the assumption that less than a half of the new cells inherit the cycle lengths of their mother cells and it is proved the existence of an asynchronous exponential growth (i.e. the tendency of a cell population to grow exponentially in a way that disperses its initial distribution toward distributions with characteristic properties) with the methods of semigroup theory and the spectral analysis of linear operators.