Heteroclinic connections for nonlocal equations

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Abstract

We construct heteroclinic orbits for a strongly nonlocal integro-differential equation. Since the energy associated to the equation is infinite in such strongly nonlocal regime, the proof, based on variational methods, relies on a renormalized energy functional, exploits a perturbation method of viscosity type, combined with an auxiliary penalization method, and develops a free boundary theory for a double obstacle problem of mixed local and nonlocal type. The description of the stationary positions for the atom dislocation function in a perturbed crystal, as given by the Peierls-Nabarro model, is a particular case of the result presented.

Original languageEnglish
Article number1950055
JournalMathematical Models and Methods in Applied Sciences
DOIs
Publication statusE-pub ahead of print - 26 Nov 2019

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