Dislocation dynamics with a mean curvature term: short time existence and uniqueness

Abstract

In this paper, we study a new model for dislocation dynamics with a mean curvature term. The model is a non-local Hamilton-Jacobi equation. We prove a short time existence and uniqueness result for this equation. We also prove a Lipschitz estimate in space and an estimate of the modulus of continuity in time for the solution.