Analysis of a Population Model Structured by the Cells Molecular Content

Marie Doumic-Jauffret (1)

1 BANG - Nonlinear Analysis for Biology and Geophysical flows

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 \cite{CBBP1}; an application to the non-linear problem is also given, leading to robust subpolynomial growth of the total population.

Mots clés: structured populations; cell division; relative entropy; long-time asymptotic; eigenproblem; transport equation

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Marie Doumic-Jauffret. Analysis of a Population Model Structured by the Cells Molecular Content. Mathematical Modelling of Natural Phenomena, 2007, 2 (3), pp.121-152. ⟨10.1051/mmnp:2007006⟩. ⟨hal-00327131⟩