75 citations · 232 across the 10 of their papers we have counts for
10 papers
Existence of solutions to the voltage-conductance kinetic equation in a general conductivity regime
C Fonte Sanchez, S Mischler, D Salort
We establish the existence of a weak solution to the Voltage-Conductance kinetic equation for any conductivity parameter and any reasonable initial datum, and in particular without…
Self-similarity and diffusive limits for linear kinetic equations: a Wild sum approach
José A. Cañizo, Stéphane Mischler, Niccolò Tassi
We prove that linear collisional kinetic equations in the whole space without confinement mechanism display a long-time self-similar behaviour. This drastically improves the recent…
Optimal decay rates for linear kinetic equations in the half-space
Émeric Bouin, Stéphane Mischler, Clément Mouhot
We prove that solutions to linear kinetic equations in a half-space with absorbing boundary conditions decay for large times like in a weighted $\sfL…
On the Voltage-Conductance kinetic equation
Claudia Fonte Sánchez, Stéphane Mischler
We consider the nonlinear Voltage-Conductance kinetic equation arising in neuroscience. We establish the existence of solutions in a weighted framework in a weak interac…
Weak and strong connectivity regimes for a general time elapsed neuron network model
Stéphane Mischler, Cristobal Quiñinao, Qilong Weng
For large fully connected neuron networks, we study the dynamics of homogenous assemblies of interacting neurons described by time elapsed models. Under general assumptions on the…
On a kinetic FitzHugh-Nagumo model of neuronal network
Stéphane Mischler, Cristóbal Quiñinao, Jonathan Touboul
We investigate existence and uniqueness of solutions of a McKean-Vlasov evolution PDE representing the macroscopic behaviour of interacting Fitzhugh-Nagumo neurons. This equation i…
Exponential stability of slowly decaying solutions to the kinetic Fokker-Planck equation
S Mischler, C Mouhot
The aim of the present paper is twofold:(1) We carry on with developing an abstract method for deriving decay estimates on the semigroup associated to non-symmetric operators in Ba…
About Kac's Program in Kinetic Theory
Stéphane Mischler, Clément Mouhot
In this Note we present the main results from the recent work arxiv:1107.3251, which answers several conjectures raised fifty years ago by Kac. There Kac introduced a many-particle…
Stability, convergence to self-similarity and elastic limit for the Boltzmann equation for inelastic hard spheres
Stéphane Mischler, Clément Mouhot
We consider the spatially homogeneous Boltzmann equation for {\em inelastic hard spheres}, in the framework of so-called {\em constant normal restitution coefficients} …
Cooling process for inelastic Boltzmann equations for hard spheres, Part I: The Cauchy problem
Stéphane Mischler, Clément Mouhot, Mariano Rodriguez Ricard
We develop the Cauchy theory of the spatially homogeneous inelastic Boltzmann equation for hard spheres, for a general form of collision rate which includes in particular variable…