On three-phase boundary motion and the singular limit of a vector-valued Ginzburg-Landau equation
journal contributionposted on 01.01.1992 by Lia Bronsard, Fernando Reitich
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Abstract: "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."