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