Browsing by Author "Van Brunt, B"
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- ItemCELL DIVISION AND THE PANTOGRAPH EQUATION(1/09/2018) Lynch, T; Van Brunt, B; Zaidi, AASimple 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.
- ItemA cell growth model revisited(Research Institute, College of Judea and Samaria,, 2012) Derfel, G; Van Brunt, B; Wake, Graeme C.In this paper a stochastic model for the simultaneous growth and division of a cell-population cohort structured by size is formulated. This probabilistic approach gives straightforward proof of the existence of the steady-size distribution and a simple derivation of the functional-differential equation for it. The latter one is the celebrated pantograph equation (of advanced type). This firmly establishes the existence of the steady-size distribution and gives a form for it in terms of a sequence of probability distribution functions. Also it shows that the pantograph equation is a key equation for other situations where there is a distinct stochastic framework.