We study the problem of large time existence of solutions for a mathematical model describingdislocation dynamics in crystals. The mathematical model is a geometric and non local eikonal
equation which does not preserve the inclusion. Under the assumption that the dislocation line is
expanding, we prove existence and uniqueness of the solution in the framework of discontinuous
viscosity solutions. We also show that this solution satisfies some variational properties, which
allows to prove that the energy associated to the dislocation dynamics is non
increasing.