1 citations · 2 across the 11 of their papers we have counts for
11 papers
Discrete hypocoercive estimates for discontinuous Galerkin methods: application to the Vlasov-Poisson-Fokker-Planck system
Yi Cai, Alain Blaustein, Tao Xiong +1
We develop and analyze a class of structure-preserving discontinuous Galerkin schemes for the nonlinear Vlasov-Poisson-Fokker-Planck model, reformulated as a hyperbolic system thro…
Existence of solutions and uniform bounds for the stationary semiconductor equations with generation and ionic carriers
Dilara Abdel, Alain Blaustein, Claire Chainais-Hillairet +2
We consider a stationary drift-diffusion system with ionic charge carriers and external generation of electron and hole charge carriers. This system arises, among other application…
A structure and asymptotic preserving scheme for the quasineutral limit of the Vlasov-Poisson system
Alain Blaustein, Giacomo Dimarco, Francis Filbet +1
In this work, we propose a new numerical method for the Vlasov-Poisson system that is both asymptotically consistent and stable in the quasineutral regime, i.e. when the Debye leng…
Longtime and chaotic dynamics in microscopic systems with singular interactions
Alexis Béjar-López, Alain Blaustein, Pierre-Emmanuel Jabin +1
This paper investigates the long time dynamics of interacting particle systems subject to singular interactions. We consider a microscopic system of interacting point particles…
Derivation of the bacterial run-and-tumble kinetic model : quantitative and strong convergence results
Alain Blaustein
During the past century, biologists and mathematicians investigated two mechanisms underlying bacteria motion: the run phase during which bacteria move in straight lines and the tu…
A structure and asymptotic preserving scheme for the Vlasov-Poisson-Fokker-Planck model
Alain Blaustein, Francis Filbet
We propose a numerical method for the Vlasov-Poisson-Fokker-Planck model written as an hyperbolic system thanks to a spectral decomposition in the basis of Hermite functions with r…
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…
Diffusive limit of the Vlasov-Poisson-Fokker-Planck model: quantitative and strong convergence results
Alain Blaustein
This work tackles the diffusive limit for the Vlasov-Poisson-Fokker-Planck model. We derive a priori estimates which hold without restriction on the phase-space dimension and propo…
Concentration profiles in FitzHugh-Nagumo neural networks: A Hopf-Cole approach
Alain Blaustein, Emeric Bouin
In this paper we focus on a spatially extended FitzHugh-Nagumo model with interactions. In the regime where strong and local interactions dominate, we quantify how the probability…
Large coupling in a FitzHugh-Nagumo neural network: quantitative and strong convergence results
Alain Blaustein
We consider a mesoscopic model for a spatially extended FitzHugh-Nagumo neural network and prove that in the regime where short-range interactions dominate, the probability density…
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…