Homogenization of the Peierls–Nabarro model for dislocation dynamics

This paper is concerned with a result of homogenization of an integro-differential equation describing dislocation dynamics. Our model involves both an anisotropic Lévy operator of order 1 and a potential depending periodically on u/ϵ. 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.