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arXiv · 2607.22112

Existence of solutions to the voltage-conductance kinetic equation in a general conductivity regime

C Fonte Sanchez·S Mischler·D Salort
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Abstract

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 smallness condition as it was the case in [9]. The proof is based on some a priori estimates mainly drawn from [15], some trace results adapted from [14] and a DiPerna-Lions weak stability argument.

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C Fonte Sanchez, S Mischler, D Salort. 2026-07-24. Existence of solutions to the voltage-conductance kinetic equation in a general conductivity regime. https://arxiv.org/abs/2607.22112

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