Analysis of a Population Model Structured by the Cells Molecular Content

Doumic, M.. "Analysis of a Population Model Structured by the Cells Molecular Content." Mathematical Modelling of Natural Phenomena 2.3 (2010): 121-152. <http://eudml.org/doc/222436>.

@article{Doumic2010,
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 [6]; an application to the non-linear problem is also given, leading to robust subpolynomial growth of the total population.},
author = {Doumic, M.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {structured populations; cell division; relative entropy; long-time asymptotic; eigenproblem; transport equation; transport equation},
language = {eng},
month = {3},
number = {3},
pages = {121-152},
publisher = {EDP Sciences},
title = {Analysis of a Population Model Structured by the Cells Molecular Content},
url = {http://eudml.org/doc/222436},
volume = {2},
year = {2010},
}

TY - JOUR
AU - Doumic, M.
TI - Analysis of a Population Model Structured by the Cells Molecular Content
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/3//
PB - EDP Sciences
VL - 2
IS - 3
SP - 121
EP - 152
AB - 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.
LA - eng
KW - structured populations; cell division; relative entropy; long-time asymptotic; eigenproblem; transport equation; transport equation
UR - http://eudml.org/doc/222436
ER -