Analysis of a Population Model Structured by the Cells Molecular Content
Mathematical modelling of natural phenomena, Tome 2 (2007) no. 3, pp. 121-152
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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.
@article{10_1051_mmnp:2007006,
author = {M. Doumic},
title = {Analysis of a {Population} {Model} {Structured} by the {Cells} {Molecular} {Content}},
journal = {Mathematical modelling of natural phenomena},
pages = {121--152},
publisher = {mathdoc},
volume = {2},
number = {3},
year = {2007},
doi = {10.1051/mmnp:2007006},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/mmnp:2007006/}
}
TY - JOUR AU - M. Doumic TI - Analysis of a Population Model Structured by the Cells Molecular Content JO - Mathematical modelling of natural phenomena PY - 2007 SP - 121 EP - 152 VL - 2 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.1051/mmnp:2007006/ DO - 10.1051/mmnp:2007006 LA - en ID - 10_1051_mmnp:2007006 ER -
%0 Journal Article %A M. Doumic %T Analysis of a Population Model Structured by the Cells Molecular Content %J Mathematical modelling of natural phenomena %D 2007 %P 121-152 %V 2 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.1051/mmnp:2007006/ %R 10.1051/mmnp:2007006 %G en %F 10_1051_mmnp:2007006
M. Doumic. Analysis of a Population Model Structured by the Cells Molecular Content. Mathematical modelling of natural phenomena, Tome 2 (2007) no. 3, pp. 121-152. doi: 10.1051/mmnp:2007006
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