Math. Model. Nat. Phenom.
Volume 2, Number 3, 2007Cancer modelling
|Page(s)||121 - 152|
|Published online||15 June 2008|
Analysis of a Population Model Structured by the Cells Molecular Content
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: email@example.com
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 ; an application to the non-linear problem is also given, leading to robust subpolynomial growth of the total population.
Mathematics Subject Classification: 35A05 / 35P05 / 92D25 / 70K20
Key words: structured populations / cell division / relative entropy / long-time asymptotic / eigenproblem / transport equation
© EDP Sciences, 2007
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