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Melting of a bicrystal along the grain boundary is discussed. A triple junction plays a crucial role in the velocity selection problem in this case. In some range of the parameters an entirely analytical solution of this problem is given. This allows to present a transparent picture of the structure of the selection theory. We also discuss the selection problem in the case of the growth of a ``eutectoid dendrite'' where a triple junction is present because three phases are involved in the eutectoid reaction.
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