Dislocation Dynamics: a Non-local Moving Boundary
Pierre Cardaliaguet, Francesca Da Lio, Nicolas Forcadel, Régis Monneau · International series of numerical mathematics · 2006
In this article, we present briefly the mathematical study of the dynamics of line defects called dislocations, in crystals. The mathematical model is an eikonal equation describing the motion of the dislocation line with a velocity which is a non-local function of the whole shape of the dislocation. We present some partial existence and uniqueness results. Finally we also show that the self-dynamics of a dislocation line at large scale is asymptotically described by an anisotropic mean curvature motion.