187 citations · 1.1k across the 80 of their papers we have counts for
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On a voltage-conductance kinetic system for integrate and fire neural networks
Benoit Perthame, Delphine Salort
The voltage-conductance kinetic equation for integrate and fire neurons has been used in neurosciences since a decade and describes the probability density of neurons in a network.…
Scalar conservation laws with rough (stochastic) fluxes
Pierre-Louis Lions, Benoit Perthame, Panagiotis E. Souganidis
We develop a pathwise theory for scalar conservation laws with quasilinear multiplicative rough path dependence, a special case being stochastic conservation laws with quasilinear…
Data Assimilation for hyperbolic conservation laws. A Luenberger observer approach based on a kinetic description
Anne-Céline Boulanger, Philippe Moireau, Benoit Perthame +1
Developing robust data assimilation methods for hyperbolic conservation laws is a challenging subject. Those PDEs indeed show no dissipation effects and the input of additional inf…
Time fluctuations in a population model of adaptive dynamics
Sepideh Mirrahimi, Benoit Perthame, Panagiotis E. Souganidis
We study the dynamics of phenotypically structured populations in environments with fluctuations. In particular, using novel arguments from the theories of Hamilton-Jacobi equation…
The Hele-Shaw asymptotics for mechanical models of tumor growth
Benoît Perthame, Fernando Quirós, Juan Luis Vázquez
Models of tumor growth, now commonly used, present several levels of complexity, both in terms of the biomedical ingredients and the mathematical description. The simplest ones con…