1 citations · 2 across the 11 of their papers we have counts for
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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…