Dynamics for Screw Dislocations with Antiplane Shear

I will discuss the motion of screw dislocations in an elastic body under antiplane shear. In this setting, dislocations are viewed as points in a two-dimensional domain where the strain field fails to be a gradient. The motion is determined by the Peach-Koehler force and the slip-planes in the material. This leads to a system of discontinuous ODE, where the vector field depends on the solution to an elliptic PDE with Neumann data. We show short-time existence of solutions; we also have uniqueness for a restricted class of domains. In general, global solutions do not exist because of collisions.