ON 3-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 thr ee-phase boundary motion as a singular limit of a vector-valued Ginzbu rg-Landau equation. We prove short-time existence and uniqueness of so lutions for this model, that is, for a system of three-phase boundarie s undergoing curvature motion with assigned angle conditions at the me eting point. Such models pertain to grain-boundary motion in alloys. T he method we use, based on linearization about the initial conditions, applies to a wide class of parabolic systems. We illustrate this furt her by its application to an eutectic solidification problem.