Skip to Main content Skip to Navigation
Journal articles

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.
Document type :
Journal articles
Complete list of metadata

Cited literature [28 references]  Display  Hide  Download
Contributor : Hugo Martin Connect in order to contact the contributor
Submitted on : Friday, March 23, 2018 - 7:19:27 PM
Last modification on : Friday, July 8, 2022 - 10:10:28 AM
Long-term archiving on: : Thursday, September 13, 2018 - 5:23:49 AM


Files produced by the author(s)



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⟩



Record views


Files downloads