Existence of pulses in excitable media with nonlocal coupling

Grégory Faye, Arnd Scheel

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)400-456
Number of pages57
JournalAdvances in Mathematics
Volume270
DOIs
StatePublished - Jan 2 2015

Bibliographical note

Publisher Copyright:
© 2014 Elsevier Inc.

Keywords

  • FitzHugh-Nagumo system
  • Fredholm operators
  • Nonlocal equation
  • Traveling wave

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