An existence and uniqueness principle for a nonlinear version of the Lebowitz‐Rubinow model with infinite maximum cycle length

Abstract

The present article deals with existence and uniqueness results for a nonlinear evolution initial-boundary value problem, which originates in an age-structured cell population model introduced by Lebowitz and Rubinow (1974) describing the growth of a cell population. Cells of this population are distinguished by age a and cycle length l. In our framework, daughter and mother cells are related by a general reproduction rule that covers all known biological ones. In this paper, the cycle length l is allowed to be infinite. This hypothesis introduces some mathematical difficulties. We consider both local and nonlocal boundary conditions.