Geodesic
Analysis of a Population Model Structured by the Cells Molecular Content
M. Doumic1, 2
1 Département de Mathématiques et Applications, École Normale Supérieure 75230 Paris cedex 05, France
2 INRIA Rocquencourt, Domaine de Voluceau, BP 105, 78153 Rocquencourt, France
Mathematical modelling of natural phenomena, Tome 2 (2007) no. 3, pp. 121-152.

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We study the mathematical properties of a general model of cell division structured with several internal variables. We begin with a simpler and specific model with two variables, we solve the eigenvalue problem with strong or weak assumptions, and deduce from it the long-time convergence. The main difficulty comes from natural degeneracy of birth terms that we overcome with a regularization technique. We then extend the results to the case with several parameters and recall the link between this simplified model and the one presented in [6]; an application to the non-linear problem is also given, leading to robust subpolynomial growth of the total population.
DOI : 10.1051/mmnp:2007006

M. Doumic 1, 2

1 Département de Mathématiques et Applications, École Normale Supérieure 75230 Paris cedex 05, France
2 INRIA Rocquencourt, Domaine de Voluceau, BP 105, 78153 Rocquencourt, France 
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M. Doumic. Analysis of a Population Model Structured by the Cells Molecular Content. Mathematical modelling of natural phenomena, Tome 2 (2007) no. 3, pp. 121-152. doi : 10.1051/mmnp:2007006. http://geodesic.mathdoc.fr/articles/10.1051/mmnp:2007006/

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