Global solution for a non-local eikonal equation modelling dislocation dynamics

In this paper, we study a non-local eikonal equation that arises from the theory of dislocation dynamics. For this equation, the global existence and uniqueness are available only for Lipschitz continuous viscosity solutions in some particular cases. Based on a new gradient entropy estimate, we prove the global existence of a continuous viscosity solution of this equation, considering non-signed velocity.