187 citations · 1.1k across the 80 of their papers we have counts for
6 papers · 2 filters
Fast reaction limit with nonmonotone reaction function
Benoît Perthame, Jakub Skrzeczkowski
We analyse fast reaction limit in the reaction-diffusion system with nonmonotone reaction function and one non-diffusing component. As speed of reaction tends to infinity, the conc…
The Aronson-Bénilan Estimate in Lebesgue Spaces
Giulia Bevilacqua, Benoît Perthame, Markus Schmidtchen
In a celebrated three-pages long paper in 1979, Aronson and Bénilan obtained a remarkable estimate on second order derivatives for the solution of the porous media equation. Since…
Invasion fronts and adaptive dynamics in a model for the growth of cell populations with heterogeneous mobility
Tommaso Lorenzi, Benoît Perthame, Xinran Ruan
We consider a model for the dynamics of growing cell populations with heterogeneous mobility and proliferation rate. The cell phenotypic state is described by a continuous structur…
Existence of a global weak solution for a reaction-diffusion problem with membrane conditions
Giorgia Ciavolella, Benoît Perthame
Several problems, issued from physics, biology or the medical science, lead to parabolic equations set in two sub-domains separated by a membrane with selective permeability to spe…
Dynamics of concentration in a population model structured by age and a phenotypical trait
Samuel Nordmann, Benoît Perthame, Cécile Taing
We study a mathematical model describing the growth process of a population structured by age and a phenotypical trait, subject to aging, competition between individuals and rare m…
Dynamics of concentration in a population structured by age and a phenotypic trait with mutations. Convergence of the corrector
Samuel Nordmann, Benoît Perthame
We study an equation structured by age and a phenotypic trait describing the growth process of a population subject to aging, competition between individuals, and mutations. This l…