In this work, we complete a study started earlier in [1,2] wherein a model of growing bacterial population has been the matter of a mathematical analysis. We show that the full model is governed by a strongly continuous semigroup. Beside the positivity and the irreducibility of the generated semigroup, we describe its asymptotic behavior in the uniform topology which leads to the asynchronous exponential growth of the bacterial population.
Submitted October 2, 2013. Published January 7, 2014.
Math Subject Classifications: 92C37, 82D75.
Key Words: Cell population dynamic; asynchronous exponential growth; semigroup.
A corrigendum was posted on October 29, 2014. It modifies the proof of Proposition 4.3. See the last page of this article.
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| Mohamed Boulanouar |
LMCM-RSA, Universite de Poitiers
86000 Poitiers, France
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