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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Pierre Gabriel, Hugo Martin. Steady distribution of the incremental model for bacteria proliferation. Networks and Heterogeneous Media, AIMS-American Institute of Mathematical Sciences, 2019, Special issue on mathematical methods in systems biology, 14 (1), pp.149-171. ⟨10.3934/nhm.2019008⟩. ⟨hal-01742140⟩

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