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

C Fonte Sanchez, S Mischler, D Salort

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.

Disclosure

“kshop in Ile-Rousse, February 2025, where this investigation project started, as well as the LJK, university of Greno- ble, for its kind hospitality. D. Salort is supported by the fundation Cino and Simone Del Duca, Institut de France. The Claude AI has been used to help proofread typos. It also suggested a classical convergence result which enabled us to make slightly shorter and simpler the proof of the trace Theorem 3.2. Apart from that, the text in this paper was fully generate”
PDF page 4

Classification: Proof ideas or individual proof-step assistance
Multiplier: 8
Verified: 2026-08-23T19:08:04.441312Z

Structural counts

Pages 26 pdf

Theorems 7 source

Lemmas 1 source

Propositions 4 source

Corollaries 2 source

Definitions 1 source

Displayed equations 79 source

Bibliography entries 15 source

Appendix pages 0 estimated

Count notes

Source counts use the expanded primary TeX file ExistVCk10.tex.
Appendix pages include the first PDF page with an explicit Appendix heading through the final page.