Abstract Delay-Differential Equation Modeling Size Dependent Cell Growth and Division

摘要

A two-phase model for the growth of a single cell population structured by size is formulated and analyzed. The model takes the form of a delay-differential equation in a Banach space. Using positivity arguments, the spectrum of the infinitesimal generator of the semigroup associated with solutions is described. Under a certain condition on the growth rate of individual cells the semigroup is compact after finite time. This is used to determine the ultimate behavior of solutions and prove the existence of a stable size distribution.