Hugoniot-type conditions and weak solutions to the phase-field system

We consider a new concept of weak solutions to the phase-field equations wi th a small parameter epsilon characterizing the length of interaction. For the standard situation of a single free interface, this concept tin contras t with the common one) leads to the well-known Stefan-Gibbs-Thomson problem as epsilon--> 0. For the case of a large number M(epsilon) (M(epsilon) --> infinity as epsilon--> 0) Of free interfaces, which corresponds to the 'wa ve-train' interpretation of a 'mushy region', this concept allows us to obt ain the limit problem as epsilon --> 0.