4 papers · 1 filter
Spectral description of a cell growth and division equation
Pierre Gabriel, Bruce van Brunt, Graeme Charles Wake +1
We give a refined description of the dominant spectrum of a non-local operator that models growth and equal mitosis of cells. More precisely we look at the spectrum in half planes…
The principal eigenvalue problem for time-periodic nonlocal equations with drift
Bertrand Cloez, Adil El Abdouni, Pierre Gabriel
In this work, we consider a general time-periodic linear transport equation with integral source term. We prove the existence of a Floquet principal eigenvalue, namely a real numbe…
Asynchronous exponential growth of the growth-fragmentation equation with unbounded fragmentation rate
Etienne Bernard, Pierre Gabriel
The objective is to prove the asynchronous exponential growth of the growth-fragmentation equation in large weighted spaces and under general assumptions on the coefficients.…
Steady distribution of the incremental model for bacteria proliferation
Pierre Gabriel, Hugo Martin
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-simila…