Boletín SEMA, No 44 (2008)

Tamaño de la letra:  Pequeña  Mediana  Grande

ANALYSIS OF A CELL SYSTEM WITH FINITE DIVISIONS

B. Perthame, T. M. Touaoula

Resumen


In this paper we consider a model of cell division which describes the
continuous growth of cells and their division. The originality of the model
is to assume only a finite number of possible divisions. We are concerned
with three questions.
First, we prove both the existence of a stable steady dynamics (first
positive eigenvector) and, second, we show that the long time asymptotics
of any solution can be described by this stable steady dynamics. Our
third result concerns the limit of a high number of possible divisions; in
the particular case where the division rates are independent of the number
of earlier divisions, we show that, in this limit, we recover the classical
cell division model for equal mitosis.

Key words:
cell division equations, growth processes, general relative
entropy, asymptotic análisis

AMS subject classifications:
35B40 35F10 92D25


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