Models of Discrete and Continuous Cell Differentiation in the Framework of Transport Equation

Abstract

We introduce a class of structured population models describing cell differentiation that consists of discrete and continuous transitions. The model is defined in a framework of measure-valued solutions of a nonlinear transport equation with a growth term. To obtain ODE-type quasi-stationary node points we exploit the idea of non-Lipschitz zeroes in the velocity. This, in combination with the so-called measure-transmission conditions, allows us to prove the existence and uniqueness of solutions. Since the analysis has biological motivations, we provide examples of its application. (An erratum is attached.)