Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-28T04:25:19.762Z Has data issue: false hasContentIssue false
  • English
  • Français

Analysis of a Population Model Structuredby the Cells Molecular Content

Published online by Cambridge University Press:  15 June 2008

M. Doumic
M. Doumic*
Affiliation:
Département de Mathématiques et Applications, École Normale Supérieure 75230 Paris cedex 05, France INRIA Rocquencourt, Domaine de Voluceau, BP 105, 78153 Rocquencourt, France
*
doumic@dma.ens.fr
Get access

Abstract

We study the mathematical properties of a general model of cell division structuredwith several internal variables. We begin with a simpler and specific model with two variables, wesolve the eigenvalue problem with strong or weak assumptions, and deduce from it the long-timeconvergence. The main difficulty comes from natural degeneracy of birth terms that we overcomewith a regularization technique. We then extend the results to the case with several parameters andrecall the link between this simplified model and the one presented in [6]; an application to thenon-linear problem is also given, leading to robust subpolynomial growth of the total population.

Keywords

structured populationscell divisionrelative entropylong-time asymptoticeigenproblemtransport equation
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 2 , Issue 3: Cancer modelling , 2007 , pp. 121 - 152
Copyright
© EDP Sciences, 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)