Weak solutions to the phase field system

We consider a new concept of weak solutions to the phase field equations with a small parameter ϵ characterizing the length of interaction. For the standard situation of a single free interface, this concept (in contrast to the common one) leads to the well-known Stefan-Gibbs-Thomson problem as ϵ → 0. For the case of a large number M(ϵ) (M(ϵ) → ∞ as ϵ → 0) of free interfaces, which is related to the "wave-train" interpretation of a "mushy region", this concept allows us to obtain limiting problems as ϵ → 0.