Nonlinear integrate and fire neuron models, part II: existence, uniqueness, and asymptotics
Seminar Room 1, Newton Institute
We continue the study of Nonlinear Noisy Leaky Integrate and Fire models for neurons. In particular, we show global existence and uniqueness of the solution for the inhibitory case, together with some comments on asymptotic decay. The main idea is to reduce the equation to a Stefan-like problem with a moving free boundary and non-standard right hand side. This is joint work with J. Carrillo, M. Gualdani and M. Schonbek.