Homogenization of the Peierls-Nabarro model for dislocation dynamics
Analysis of PDEs
2012-07-19 v2
Abstract
This paper is concerned with a result of homogenization of an integro-differential equation describing dislocation dynamics. Our model involves both an anisotropic L\'{e}vy operator of order 1 and a potential depending periodically on . The limit equation is a non-local Hamilton-Jacobi equation, which is an effective plastic law for densities of dislocations moving in a single slip plane.
Keywords
Cite
@article{arxiv.1007.2915,
title = {Homogenization of the Peierls-Nabarro model for dislocation dynamics},
author = {Régis Monneau and Stefania Patrizi},
journal= {arXiv preprint arXiv:1007.2915},
year = {2012}
}
Comments
39 pages