  We discuss melting of alloys along grain boundaries as a free boundary
problem for two moving solid-liquid interfaces. One of them is the melting
front and the other is the solidification front. The presence of the triple
junction plays an important role in controlling the velocity of this process.
The interfaces strongly interact via the diffusion field in the thin liquid
layer between them. In the liquid film migration (LFM) mechanism the system
chooses a more efficient kinetic path, which is controlled by diffusion in the
liquid film on relatively short distances. However, only weak coherency strain
energy is the effective driving force for LFM in the case of melting of
one-phase alloys.
  The process with only one melting front would be controlled by the very slow
diffusion in the mother solid phase on relatively large distances.
