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A CELL GROWTH MODEL ADAPTED FOR THE MINIMUM CELL SIZE DIVISION

Part of: Functional-differential and differential-difference equations

Published online by Cambridge University Press:  01 December 2015

B. VAN BRUNT ,
S. GUL  and
G. C. WAKE
B. VAN BRUNT*
Affiliation:
Institute of Fundamental Sciences, Massey University, Palmerston North 4442, New Zealand email b.vanbrunt@massey.ac.nz, S.Gul@massey.ac.nz
S. GUL
Affiliation:
Institute of Fundamental Sciences, Massey University, Palmerston North 4442, New Zealand email b.vanbrunt@massey.ac.nz, S.Gul@massey.ac.nz
G. C. WAKE
Affiliation:
Institute of Natural and Mathematical Sciences, Massey University at Albany, P.B. 102904, North Shore MC, Auckland, New Zealand email G.C.Wake@massey.ac.nz
*
✉b.vanbrunt@massey.ac.nz
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Abstract

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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.

Keywords

pantograph equationcell growth modelfunctional differential equation

MSC classification

Primary: 34K06: Linear functional-differential equations
Secondary: 34K10: Boundary value problems
Type
Research Article
Information
The ANZIAM Journal , Volume 57 , Issue 2 , October 2015 , pp. 138 - 149
Copyright
© 2015 Australian Mathematical Society 

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