A convergent scheme for a nonlocal Hamilton Jacobi equation modelling dislocation dynamics (Q2433994)

The authors study dislocation dynamics with a level set point of view. The presented model looks at the zero level set of the solution of a nonlocal Hamilton Jacobi equation, as a dislocation in a plane of a crystal. The front has a normal speed depending on the solution itself. The authors prove existence and uniqueness for short time in the set of continuous viscosity solutions. The authors also present a first order finite difference scheme for the corresponding level set formulation of the model. Numerical results are also provided.