This work deals with a mathematical study for growing a bacterial population. Each bacterium is distinguished by its degree of maturity and its maturation velocity. Here we study the limit case corresponding to infinite maturation velocities. We show that this model is governed by a strongly continuous semigroup. We also study the lattice and spectral properties of the generated semigroup and we compute its type.
Submitted September 3, 2012. Published December 4, 2012.
Math Subject Classifications: 92C37, 82D75.
Key Words: Semigroups; positivity; irreducibility; spectral properties; cell population dynamics; general boundary condition.
An addendum was attached on June 24, 2013. It corrects some misprints. 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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