Pinning and Unpinning in Nonlocal Systems

TL;DR

This paper explores the phenomena of pinning and unpinning in nonlocal equations, revealing their differences from discrete media and analyzing asymptotics through geometric singular perturbation theory, supported by numerical evidence.

Contribution

It introduces new insights into unpinning asymptotics in nonlocal systems and examines the influence of kernel regularity on these phenomena.

Findings

Unpinning asymptotics are characterized using geometric singular perturbation theory.

Pinning phenomena in nonlocal systems differ from those in discrete media.

Kernel regularity affects unpinning behavior.

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.