ANZIAM J. 43(2002), 359–374 ANALYSIS OF CELL POPULATION PDE MODELS WITH GENERAL MATURATION RATES

This paper considers a cell population model with a general maturation rate. This model is described by a nonlinear PDE. We use the theory of operator semigroups to study the problem under simple hypotheses on the growth function and the nonlinear term. By showing that a related operator generates a strongly continuous semigroup, we prove the existence of a classical solution of the nonlinear problem and its positivity. It is also proved that under simple hypotheses, the problem generates a semiflow. The invariance of the semiflow is studied as well. 1