{
"id": "1803.04950",
"version": "v1",
"published": "2018-03-13T17:32:31.000Z",
"updated": "2018-03-13T17:32:31.000Z",
"title": "Steady distribution of the incremental model for bacteria proliferation",
"authors": [
"Pierre Gabriel",
"Hugo Martin"
],
"comment": "18 pages, 3 figures",
"categories": [
"math.AP"
],
"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 $\\mathrm{L}^1$ 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.",
"revisions": [
{
"version": "v1",
"updated": "2018-03-13T17:32:31.000Z"
}
],
"analyses": {
"subjects": [
"35Q92",
"35P05",
"45K05",
"45P05",
"92D25",
"35A22",
"35B40",
"35B65"
],
"keywords": [
"incremental model",
"bacteria proliferation",
"steady distribution",
"long time asymptotic behaviour",
"linear growth rate"
],
"note": {
"typesetting": "TeX",
"pages": 18,
"language": "en",
"license": "arXiv",
"status": "editable"
}
}
}