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	Volume 3, Issue 2 Pg 103 - 169 (May 2009)
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Advances in Differential Equations and Control Processes

Advances in Differential Equations and Control Processes
Volume 3, Issue 1, Pages 77 - 101 (February 2009)

ASYMPTOTIC BEHAVIOUR FOR A MATHEMATICAL CELLULAR MODEL WITH INFINITE CELL CYCLE LENGTH
M. Boulanouar (France)

Abstract:
In this paper, we are concerned with the cellular profile of a mathematical model of an age structured cell population endowed with general biological reproduction laws. Each cell is distinguished by its age and its cell cycle length which can be infinite. We study the positivity and irreducibility of the generated semigroup and we calculate its essential type. The cellular profile is obtained by the asymptotic behaviour in the uniform topology.

Keywords and phrases: cell population dynamics, general boundary condition, semigroups, compactness, positivity, irreducibility, asymptotic behaviour.

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