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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
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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

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