On the Voltage-Conductance kinetic equation - Statistique pour le Vivant et l’Homme
Pré-Publication, Document De Travail Année : 2024

On the Voltage-Conductance kinetic equation

Résumé

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 the flow associated to the linear (possibly time dependent) Voltage-Conductance kinetic equation.
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Dates et versions

hal-04667451 , version 1 (04-08-2024)

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  • HAL Id : hal-04667451 , version 1

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Claudia Fonte Sánchez, Stéphane Mischler. On the Voltage-Conductance kinetic equation. 2024. ⟨hal-04667451⟩
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