Unimodality of steady size distributions of growing cell populations
type: Item
instance of: scholarly article
title: Unimodality of steady size distributions of growing cell populations
zbMATH Open document ID: 1022.35078
DOI: 10.1007/PL00001379
published in: Journal of Evolution Equations
publication date: 2003-10-19T00:00:00Z
review text: The authors investigate a hyperbolic functional partial differential equation, \(n_t(x,t)=A(n)\), where \[ A(n)\equiv -(g(x)n(x,t))_x-b(x)n(x,t)+\alpha^2b(\alpha x)n(\alpha x),\quad x\in \mathbb{R}_+. \] This describes the evolution of a population of growing and dividing cells. Here a mother cell of size \(x\) divides into \(\alpha >1\) (usually \(\alpha =2\)) daughter cells of the same size \(x\). The function \(g(x)\) is the growth rate and \(b(x)\) is the division rate of a cell of size \(x\). There is no mortality of cells, so the reasonable boundary conditions for this model are \(g(0)n(0,t)=0\) and \(\lim_{x\to\infty }g(x)n(x,t)=0\) \(t>0\). The main result is that the eigenfunction \(y(x)\) of the operator \(A(n)\) is unimodal. The authors use a known result of \textit{T. Kato} and \textit{J. B. McLeod} [Bull. Am. Math. Soc. 77, 891-937 (1971; Zbl 0236.34064)] to discuss that the probability density function for the stationary size distribution is necessarily unimodal.
Mathematics Subject Classification ID: 35R10
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 1757481
zbMATH Keywords: growing and dividing cells
zbMATH Keywords: stationary size distribution
zbMATH Keywords: unimodality
author: F. P. Da Costa
author: M. Grinfeld
author: J. B. McLeod
reviewed by: Dimitar A. Kolev
MaRDI profile type: Publication
full work available at URL: pl00001379
OpenAlex ID: W2154664743
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description: scientific article; zbMATH DE number 1757481