Steady distribution of the incremental model for bacteria proliferation

Abstract : We study the mathematical properties of a model of cell division structured by two variables – the size and the size increment – in the case of a linear growth rate and a self-similar fragmentation kernel. We first show that one can construct a solution to the related two dimensional eigenproblem associated to the eigenvalue 1 from a solution of a certain one dimensional fixed point problem. Then we prove the existence and uniqueness of this fixed point in the appropriate L 1 weighted space under general hypotheses on the division rate. Knowing such an eigenfunction proves useful as a first step in studying the long time asymptotic behaviour of the Cauchy problem.
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Pré-publication, Document de travail
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Contributeur : Hugo Martin <>
Soumis le : vendredi 23 mars 2018 - 19:19:27
Dernière modification le : vendredi 16 novembre 2018 - 01:50:12
Document(s) archivé(s) le : jeudi 13 septembre 2018 - 05:23:49


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  • HAL Id : hal-01742140, version 1
  • ARXIV : 1803.04950


Pierre Gabriel, Hugo Martin. Steady distribution of the incremental model for bacteria proliferation. 2018. 〈hal-01742140〉



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