Pinning and Unpinning in Nonlocal Systems

Taylor Anderson; Grégory Faye; Arnd Scheel; David Stauffer

doi:10.1007/s10884-016-9518-6

Pinning and Unpinning in Nonlocal Systems

Taylor Anderson, Grégory Faye, Arnd Scheel, David Stauffer

School of Mathematics

Research output: Contribution to journal › Article › peer-review

13 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 language	English (US)
Pages (from-to)	897-923
Number of pages	27
Journal	Journal of Dynamics and Differential Equations
Volume	28
Issue number	3-4
DOIs	https://doi.org/10.1007/s10884-016-9518-6
State	Published - 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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10.1007/s10884-016-9518-6

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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.",

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AU - Anderson, Taylor

AU - Faye, Grégory

AU - Scheel, Arnd

AU - Stauffer, David

N1 - 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.

PY - 2016/9/1

Y1 - 2016/9/1

N2 - 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.

AB - 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.

KW - Front pinning

KW - Nonlocal coupling

KW - Singular perturbations

KW - Traveling waves

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JO - Journal of Dynamics and Differential Equations

JF - Journal of Dynamics and Differential Equations

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ER -

Pinning and Unpinning in Nonlocal Systems

Abstract

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