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A Mellin transform solution to a second-order pantograph equation with linear dispersion arising in a cell growth model

Published online by Cambridge University Press:  05 January 2011

B. van BRUNT  and
G. C. WAKE
B. van BRUNT
Affiliation:
Institute of Fundamental Sciences, Massey University Manawatu, Private Bag 11-222, Palmerston North 4442, New Zealand
G. C. WAKE
Affiliation:
Centre for Mathematics-in-Industry, Institute of Information and Mathematical Sciences, Massey University Auckland, Private Bag 102-904, NSMC, Auckland 0745, New Zealand email: [email protected]
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Abstract

In this paper we study the probability density function solutions to a second-order pantograph equation with a linear dispersion term. The functional equation comes from a cell growth model based on the Fokker–Planck equation. We show that the equation has a unique solution for constant positive growth and splitting rates and construct the solution using the Mellin transform.

Keywords

Functional differential equations, existence and uniqueness, exact solutionssteady-size distributions
Type
Papers
Information
European Journal of Applied Mathematics , Volume 22 , Issue 2 , April 2011 , pp. 151 - 168
Copyright
Copyright © Cambridge University Press 2011

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