Existence of pulses in excitable media with nonlocal coupling
Analysis of PDEs
2013-11-27 v1
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.
Keywords
Cite
@article{arxiv.1311.6508,
title = {Existence of pulses in excitable media with nonlocal coupling},
author = {Gregory Faye and Arnd Scheel},
journal= {arXiv preprint arXiv:1311.6508},
year = {2013}
}