On three-phase boundary motion and the singular limit of a vector-valued Ginzburg-Landau equation

We present a formal asymptotic analysis which suggests a model for three-phase boundary motion as a singular limit of a vector-valued Ginzburg-Landau equation. We prove short-time existence and uniqueness of solutions for this model, that is, for a system of three-phase boundaries undergoing curvature motion with assigned angle conditions at the meeting point. Such models pertain to grain-boundary motion in alloys. The method we use, based on linearization about the initial conditions, applies to a wide class of parabolic systems. We illustrate this further by its application to an eutectic solidification problem.