Long-time asymptotics for evolutionary crystal dislocations models

In this talk, I will discuss a recent result concerning the long-time behavior of solutions to evolutionary Peierls-Nabarro type equations, related to crystal dislocations.
I will present the construction of solutions that, at large times, behave like a superposi- tion of an arbitrary finite number of fundamental dislocations, equally oriented and centered near points that evolve according to a repulsive dynamical system.
This result has been obtained in collaboration with J. D ?avila and M. del Pino (University of Bath).