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math.AP2026
Existence of solutions to the voltage-conductance kinetic equation in a general conductivity regime
C Fonte Sanchez, S Mischler, D Salort
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…
math.AP2024
On the Voltage-Conductance kinetic equation
Claudia Fonte Sánchez, Stéphane Mischler
We consider the nonlinear Voltage-Conductance kinetic equation arising in neuroscience. We establish the existence of solutions in a weighted framework in a weak interac…
math.AP2023★ 2 cited
On the Krein-Rutman theorem and beyond
Claudia Fonte Sanchez, Pierre Gabriel, Stéphane Mischler
In this work, we revisit the Krein-Rutman theory for semigroups of positive operators in a Banach lattice framework and we provide some very general, efficient and handy results wi…