Analysis of a Population Model Structuredby the Cells Molecular Content

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...

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Bibliographic Details
Published in:Mathematical modelling of natural phenomena 2007, Vol.2 (3), p.121-152
Main Author: Doumic, M.
Format: Article
Language:English
Subjects:
35A05
35P05
70K20
92D25
cell division
eigenproblem
long-time asymptotic
relative entropy
structured populations
transport equation
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Summary: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.
ISSN:0973-5348
1760-6101
DOI:10.1051/mmnp:2007006