357 citations · 864 across the 37 of their papers we have counts for
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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…
Numerical Simulations to the Vlasov-Poisson System with a Strong Magnetic Field
Francis Filbet, Chang Yang
In this paper, we present an efficient Particle-In-Cell algorithm for the simulation of the three dimensional Vlasov-Poisson system in the presence of a strong external magnetic fi…
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…
Convergence of a Finite Volume Scheme for a System of Interacting Species with Cross-Diffusion
José A. Carrillo, Francis Filbet, Markus Schmidtchen
In this work we present the convergence of a positivity preserving semi-discrete finite volume scheme for a coupled system of two non-local partial differential equations with cros…
A Hybrid Discontinuous Galerkin Scheme for Multi-scale Kinetic Equations
Francis Filbet, Tao Xiong
We develop a multi-dimensional hybrid discontinuous Galerkin method for multi-scale kinetic equations. This method is based on moment realizability matrices, a concept introduced b…