Velocity selection problem in the presence of the triple junction.

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 us 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."