Analysis of a Population Model Structured by the Cells Molecular Content

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

Corresponding author: doumic@dma.ens.fr

Abstract

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.