187 citations · 1.1k across the 80 of their papers we have counts for
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A Structured Population Model of Cell Differentiation
Marie Doumic, Anna Marciniak-Czochra, Benoit Perthame +1
We introduce and analyze several aspects of a new model for cell differentiation. It assumes that differentiation of progenitor cells is a continuous process. From the mathematical…
Can a traveling wave connect two unstable states? The case of the nonlocal Fisher equation
Gregoire Nadin, Benoit Perthame, Min Tang
This note investigates the properties of the traveling waves solutions of the nonlocal Fisher equation. The existence of such solutions has been proved recently in \cite{BNPR} but…
Dirac mass dynamics in multidimensional nonlocal parabolic equations
Alexander Lorz, Sepideh Mirrahimi, Benoît Perthame
Nonlocal Lotka-Volterra models have the property that solutions concentrate as Dirac masses in the limit of small diffusion. Is it possible to describe the dynamics of the limiting…
Analysis of Nonlinear Noisy Integrate\&Fire Neuron Models: blow-up and steady states
María J. Cáceres, José A. Carrillo, Benoît Perthame
Nonlinear Noisy Leaky Integrate and Fire (NNLIF) models for neurons networks can be written as Fokker-Planck-Kolmogorov equations on the probability density of neurons, the main pa…
Traveling plateaus for a hyperbolic Keller-Segel system with attraction and repulsion: existence and branching instabilities
Benoit Perthame, Christian Schmeiser, Min Tang +1
How can repulsive and attractive forces, acting on a conservative system, create stable traveling patterns or branching instabilities? We have proposed to study this question in th…
Singular Hamilton-Jacobi equation for the tail problem
Sepideh Mirrahimi, Guy Barles, Benoit Perthame +1
In this paper we study the long time-long range behavior of reaction diffusion equations with negative square root -type reaction terms. In particular we investigate the exponentia…