Pinning and Unpinning in Nonlocal Systems

Taylor Anderson, Grégory Faye, Arnd Scheel, David Stauffer

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

We investigate pinning regions and unpinning asymptotics in nonlocal equations. We show that phenomena are related to but different from pinning in discrete and inhomogeneous media. We establish unpinning asymptotics using geometric singular perturbation theory in several examples. We also present numerical evidence for the dependence of unpinning asymptotics on regularity of the nonlocal convolution kernel.

Original languageEnglish (US)
Pages (from-to)897-923
Number of pages27
JournalJournal of Dynamics and Differential Equations
Volume28
Issue number3-4
DOIs
StatePublished - Sep 1 2016

Bibliographical note

Funding Information:
This research was conducted during Summer 2014 in the REU: Complex Systems at the University of Minnesota Department of Mathematics, funded by the National Science Foundation (DMS-1311414) and (DMS-1311740).

Publisher Copyright:
© 2016, Springer Science+Business Media New York.

Keywords

  • Front pinning
  • Nonlocal coupling
  • Singular perturbations
  • Traveling waves

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