Analysis of a Population Model Structured by the Cells Molecular Content

Marie Doumic-Jauffret 1
1 BANG - Nonlinear Analysis for Biology and Geophysical flows
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt
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.
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Submitted on : Tuesday, October 7, 2008 - 2:20:58 PM
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Marie Doumic-Jauffret. Analysis of a Population Model Structured by the Cells Molecular Content. Mathematical Modelling of Natural Phenoma, 2007, 2 (3), pp.121-152. ⟨10.1051/mmnp:2007006⟩. ⟨hal-00327131⟩

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