A model of proliferating cell populations with infinite cell cycle length: Semigroup existence
type: Item
instance of: scholarly article
title: A model of proliferating cell populations with infinite cell cycle length: Semigroup existence
zbMATH Open document ID: 1193.47042
published in: Acta Applicandae Mathematicae
publication date: 2010-05-26T00:00:00Z
review text: The paper is essentially devoted to studying the following partial differential equation \[ \frac{\partial f}{\partial t}=-\frac{\partial f}{\partial a}-\mu f \] with boundary condition \[ f(t,0,l)=[Kf(t,\cdot,\cdot)](l), \] where \(K\) is a linear operator on suitable trace spaces. The problem studied here comes from a mathematical model of an age structured cell population. The author shows that the problem is well-posed and gives the explicit expression of the generated semigroup under certain conditions on \(\mu\). A concrete example is given to illustrate the results.
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 47N60
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 5712200
zbMATH Keywords: semigroup method
zbMATH Keywords: well-posedness
zbMATH Keywords: cell population dynamics
zbMATH Keywords: boundary condition
author: Mohamed Boulanouar
MaRDI profile type: Publication
full work available at URL: s10440-008-9355-7
OpenAlex ID: W2073030620
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DOI: 10.1007/S10440-008-9355-7
description: scientific article; zbMATH DE number 5712200