Journal of Dynamics and Differential Equations

, Volume 28, Issue 3–4, pp 897–923 | Cite as

Pinning and Unpinning in Nonlocal Systems

  • Taylor Anderson
  • Grégory Faye
  • Arnd Scheel
  • David Stauffer
Article

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.

Keywords

Front pinning Singular perturbations Traveling waves Nonlocal coupling 

Notes

Acknowledgments

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).

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Taylor Anderson
    • 1
  • Grégory Faye
    • 2
    • 4
  • Arnd Scheel
    • 2
  • David Stauffer
    • 3
  1. 1.Department of Mathematics and StatisticsMount Holyoke CollegeSouth HadleyUSA
  2. 2.School of MathematicsUniversity of MinnesotaMinneapolisUSA
  3. 3.Department of MathematicsCornell UniversityIthacaUSA
  4. 4.CNRS, UMR 5219Institut de Mathématiques de ToulouseToulouse CedexFrance

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