# Analysis of a Population Model Structured by the Cells Molecular Content

Mathematical Modelling of Natural Phenomena (2010)

- Volume: 2, Issue: 3, page 121-152
- ISSN: 0973-5348

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topDoumic, 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 -

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