Simple models for size structured cell populations undergoing growth and division producea class of functional ordinary differential equations, called pantograph equations, that describe the longtime asymptotics of the cell number density. Pantograph equations arise in a number of applicationsoutside this model and, as a result, have been studied heavily over the last five decades. In this paper we review and survey the role of the pantograph equation in the context of cell division. In addition, fora simple case we present a method of solution based on the Mellin transform and establish uniqueness directly from the transform equation.
ESAIM: PROCEEDINGS AND SURVEYS, 2018, 62 pp. 158 - 167