Existence of pulses in excitable media with nonlocal coupling

2013/11/25 by Gregory Faye, Faye, Gregory, Arnd Scheel +1 · 2 citations
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1311.6508

arxiv created 2013/11/25 · arxiv updated 2013/11/27

Abstract

We prove the existence of fast traveling pulse solutions in excitable media with non-local coupling. Existence results had been known, until now, in the case of local, diffusive coupling and in the case of a discrete medium, with finite-range, non-local coupling. Our approach replaces methods from geometric singular perturbation theory, that had been crucial in previous existence proofs, by a PDE oriented approach, relying on exponential weights, Fredholm theory, and commutator estimates.

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