### 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.

entropy, asymptotic análisis

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.

**cell division equations, growth processes, general relative**

Key words:Key words:

entropy, asymptotic análisis

**35B40 35F10 92D25**

AMS subject classifications:AMS subject classifications:

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