357 citations · 864 across the 37 of their papers we have counts for
8 papers · 1 filter
On a discrete framework of hypocoercivity for kinetic equations
Alain Blaustein, Francis Filbet
We propose and study a fully discrete finite volume scheme for the Vlasov-Fokker-Planck equation written as an hyperbolic system using Hermite polynomials in velocity. This approac…
Concentration phenomena in Fitzhugh-Nagumo's equations: A mesoscopic approach
Alain Blaustein, Francis Filbet
We consider a spatially extended mesoscopic FitzHugh-Nagumo model with strong local interactions and prove that its asymptotic limit converges towards the classical nonlocal reacti…
Asymptotics of the three dimensional Vlasov equation in the large magnetic field limit
Francis Filbet, Luis Miguel Rodrigues
We study the asymptotic behavior of solutions to the Vlasov equation in the presence of a strong external magnetic field. In particular we provide a mathematically rigorous derivat…
Rigorous derivation of the nonlocal reaction-diffusion FitzHugh-Nagumo system
Joachim Crevat, Grégory Faye, Francis Filbet
We introduce a spatially extended transport kinetic FitzHugh-Nagumo model with forced local interactions and prove that its hydrodynamic limit converges towards the classical nonlo…
On the asymptotic limit of the three dimensional Vlasov-Poisson system for large magnetic field : formal derivation
Pierre Degond, Francis Filbet
This paper establishes the long time asymptotic limit of the three dimensional Vlasov-Poisson equation with strong external magnetic field. The guiding center approximation is inve…
A Rescaling Velocity Method for Dissipative Kinetic Equations - Applications to Granular Media
Francis Filbet, Thomas Rey
We present a new numerical algorithm based on a relative energy scaling for collisional kinetic equations allowing to study numerically their long time behavior, without the usual…
Analysis of spectral methods for the homogeneous Boltzmann equation
Francis Filbet, Clément Mouhot
The development of accurate and fast algorithms for the Boltzmann collision integral and their analysis represent a challenging problem in scientific computing and numerical analys…
Solving the Boltzmann equation in N log N
Francis Filbet, Clément Mouhot, Lorenzo Pareschi
In [C. Mouhot and L. Pareschi, "Fast algorithms for computing the Boltzmann collision operator," Math. Comp., to appear; C. Mouhot and L. Pareschi, C. R. Math. Acad. Sci. Paris, 33…