4 papers · 1 filter
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…
Optimal decay rates for linear kinetic equations in the half-space
Ãmeric 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…
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…
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…