Analysis of a Population Model Structured by the Cells Molecular Content - Archive ouverte HAL Access content directly
Journal Articles Mathematical Modelling of Natural Phenomena Year : 2007

Analysis of a Population Model Structured by the Cells Molecular Content

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 \cite{CBBP1}; an application to the non-linear problem is also given, leading to robust subpolynomial growth of the total population.
Fichier principal
Vignette du fichier
cyclin_DEF4_211107.pdf (556.39 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-00327131 , version 1 (07-10-2008)

Identifiers

Cite

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⟩
201 View
172 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More