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ASYMMETRICAL CELL DIVISION WITH EXPONENTIAL GROWTH

Part of: Miscellaneous topics - Partial differential equations

Published online by Cambridge University Press:  04 June 2021

A. A. ZAIDI Open the ORCID record for A. A. ZAIDI [Opens in a new window]  and
B. VAN BRUNT Open the ORCID record for B. VAN BRUNT [Opens in a new window]
A. A. ZAIDI*
Affiliation:
Department of Mathematics, Lahore University of Management Sciences, Lahore, Pakistan
B. VAN BRUNT
Affiliation:
School of Fundamental Sciences, Massey University, Palmerston North, New Zealand; B.vanBrunt@massey.ac.nz.
*
Email: ali.zaidi@lums.edu.pk
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Abstract

An advanced pantograph-type partial differential equation, supplemented with initial and boundary conditions, arises in a model of asymmetric cell division. Methods for solving such problems are limited owing to functional (nonlocal) terms. The separation of variables entails an eigenvalue problem that involves a nonlocal ordinary differential equation. We discuss plausible eigenvalues that may yield nontrivial solutions to the problem for certain choices of growth and division rates of cells. We also consider the asymmetric division of cells with linear growth rate which corresponds to “exponential growth” and exponential rate of cell division, and show that the solution to the problem is a certain Dirichlet series. The distribution of the first moment of the biomass is shown to be unimodal.

Keywords

nonlocal partial differential equationsfunctional partial differential equations

MSC classification

Primary: 35R10: Partial functional-differential equations
Type
Research Article
Information
The ANZIAM Journal , Volume 63 , Issue 1 , January 2021 , pp. 70 - 83
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Copyright
© Australian Mathematical Society 2021

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