On the Theory of a Growing Cell Population with Zero Minimum Cycle Length

Abstract

This paper deals with the Leibowitz-Rubinow models of population dynamics with general birth laws and zero minimum cycle length. We give generation results in L p -spaces and investigate the spectrum and the asymptotic behavior of the corresponding c 0 -semigroup.  2002 Elsevier Science

Spectral Distribution of Transport Operator Arising in Growing Cell Populations

“…For the past few years, there are many research works on the spectrum analysis of (1), and some of them had been discussed in [6,[10][11][12][13][14][15][16]. Jeribi et al [10] discussed Rotenberg's model of cell population with general compact boundary conditions and proved that the transport semigroup was irreducible, and a spectral decomposition of the solution into an asymptotic term was derived.…”

Semigroup generation propertiesof streaming operators with noncontractive boundary conditions

“…⋄ Remark 5.2. It is possible to exhibit similar examples from neutron transport models with specular reflection conditions [32] and for transport-like equations from population dynamics [19] (see also Example 2.6 below).…”

“…Let us explain the strategy we follow to prove this result. This strategy is inspired by a model from population dynamics (see Example 2.6) studied together with M. Mokhtar-Kharroubi [19]. Our aim is to prove that the following evolution problem…”

An existence and uniqueness principle for a nonlinear version of the Lebowitz‐Rubinow model with infinite maximum cycle length

“…All biological laws of the transition for distribution of mother cells with cycle length l to daughter cells with cycle length l are mathematically described by the general boundary operator R (for examples of boundary operators R we refer the reader to the literature). It should be noticed that several mathematical aspects concerning the linear Cauchy problem and , well‐posedness (generation results), spectral analysis, time asymptotic behavior of solution (when it exists) were discussed in many papers (we refer, for example, to the works of previous studies and the references therein).…”