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ON A CELL DIVISION EQUATION WITH A LINEAR GROWTH RATE

Published online by Cambridge University Press:  26 February 2018

B. VAN BRUNT
Affiliation:
Institute of Fundamental Sciences, Massey University, Palmerston North, New Zealand email [email protected], [email protected], [email protected]
A. ALMALKI
Affiliation:
Institute of Fundamental Sciences, Massey University, Palmerston North, New Zealand email [email protected], [email protected], [email protected]
T. LYNCH
Affiliation:
Institute of Fundamental Sciences, Massey University, Palmerston North, New Zealand email [email protected], [email protected], [email protected]
A. ZAIDI*
Affiliation:
Department of Mathematics, Lahore University of Management Sciences, Lahore, Pakistan email [email protected]
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Abstract

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We consider an initial–boundary value problem that involves a partial differential equation with a functional term. The problem is motivated by a cell division model for size structured cell cohorts in which growth and division occur. Although much is known about the large time asymptotic behaviour of solutions to these problems for constant growth rates, general solution techniques are rare. We analyse the case where the growth rate is linear and the division rate is a monomial, and we develop a method to determine the general solution for a general class of initial data. The large time dynamics of solutions for this case are significantly different from the constant growth rate case. We show that solutions approach a time-dependent attracting solution that is periodic in the time variable.

Type
Research Article
Copyright
© 2018 Australian Mathematical Society 

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