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.
Bibliographical noteFunding 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).
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- Front pinning
- Nonlocal coupling
- Singular perturbations
- Traveling waves