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Autori principali: Sánchez, Claudia Fonte, Mischler, Stéphane
Natura: Preprint
Pubblicazione: 2024
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Accesso online:https://arxiv.org/abs/2408.02471
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author Sánchez, Claudia Fonte
Mischler, Stéphane
author_facet Sánchez, Claudia Fonte
Mischler, Stéphane
contents We consider the nonlinear Voltage-Conductance kinetic equation arising in neuroscience. We establish the existence of solutions in a weighted $L^\infty$ 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.
format Preprint
id arxiv_https___arxiv_org_abs_2408_02471
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle On the Voltage-Conductance kinetic equation
Sánchez, Claudia Fonte
Mischler, Stéphane
Analysis of PDEs
We consider the nonlinear Voltage-Conductance kinetic equation arising in neuroscience. We establish the existence of solutions in a weighted $L^\infty$ 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.
title On the Voltage-Conductance kinetic equation
topic Analysis of PDEs
url https://arxiv.org/abs/2408.02471