Claudia Sanchez
Biography
Université Paris Dauphine
Short Bio:
Université Paris Dauphine
Title:
On the voltage-conductance kinetic equation.
Abstract:
This talk delves into the non-linear kinetic Voltage-Conductance equation, a crucial mathematical model for understanding neuronal activity. We obtain two key results in a framework suitable for weak interactions. First, we establish the existence of solutions. Second, we prove linear asymptotic exponential stability of the steady state. This stability result builds upon a recent estimate by Dou (2023) and offers a constructive approach. Both results are based in a fundamental way on some ultracontractivity property of the flow associated to the linear of the Voltage-Conductance equation.
