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arXiv · 1311.6508

Existence of pulses in excitable media with nonlocal coupling

Gregory Faye·Arnd Scheel
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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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Gregory Faye, Arnd Scheel. 2013-11-25. Existence of pulses in excitable media with nonlocal coupling. https://arxiv.org/abs/1311.6508

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