Séance Séminaire

Séminaire ACSIOM

Existence of traveling pulse solutions in excitable media with nonlocal coupling

In this talk, we prove the existence of fast traveling pulses for a class of FitzHugh-Nagumo equations with nonlocal diffusion. Unlike the dynamical systems approach via geometric singular perturbation theory (Fenichel's theorem and Exchange Lemma), our proof relies on matched asymptotics techniques and Fredholm properties of differential operators on suitable Banach spaces (Spectral Flow and Nonlocal Exchange Lemma). This is joint work this Arnd Scheel.