Abstract
We consider the equation
We study the evolution of such dislocation function for macroscopic space and time scales, namely we introduce the function
We show that, for small ϵ, the function v ϵ approaches the sum of step functions. From the physical point of view, this shows that the dislocations have the tendency to concentrate at single points of the crystal, where the size of the slip coincides with the natural periodicity of the medium. We also show that the motion of these dislocation points is governed by an interior repulsive potential that is superposed to an elastic reaction to the external stress.