A cell growth model adapted for the minimum cell size division

Bruce van Brunt, Saima Gul, Graeme Charles Wake

Abstract


We study a cell growth model with a division function that models cells which divide only after they have reached a certain minimum size. In contrast to the cases studied in the literature, the determination of the steady size distribution entails an eigenvalue that is not known explicitly, but is defined through a continuity condition. We show that there is a steady size distribution solution to this problem.


doi:10.1017/S1446181115000218

Keywords


pantograph equation; cell growth model; functional differential equation



DOI: http://dx.doi.org/10.21914/anziamj.v57i0.9061



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.