On the Voltage-Conductance kinetic equation
Analysis of PDEs
2024-08-06 v1
Abstract
We consider the nonlinear Voltage-Conductance kinetic equation arising in neuroscience. We establish the existence of solutions in a weighted framework in a weak interaction regime. We also prove the linear asymptotic exponential stability of the steady state making constructive a recent estimate of Xu'an Dou et al. (2023). Both results are based in a fundamental way on some ultracontractivity property of theflow associated to the linear (possibly time dependent) Voltage-Conductance kinetic equation.
Cite
@article{arxiv.2408.02471,
title = {On the Voltage-Conductance kinetic equation},
author = {Claudia Fonte Sánchez and Stéphane Mischler},
journal= {arXiv preprint arXiv:2408.02471},
year = {2024}
}