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Heteroclinic connections for nonlocal equations.
- Source :
-
Mathematical Models & Methods in Applied Sciences . Dec2019, Vol. 29 Issue 14, p2585-2636. 52p. - Publication Year :
- 2019
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02182025
- Volume :
- 29
- Issue :
- 14
- Database :
- Academic Search Index
- Journal :
- Mathematical Models & Methods in Applied Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 141276897
- Full Text :
- https://doi.org/10.1142/S0218202519500556