Phase change without sharp interfaces

It is well known that the classical description of melting/solidification processes leads to a mathematical problem in which the regions occupied by the two phases are separated by a sharp interface, the free boundary. On such an interface the temperature u is set equal to the phase-change temperature (which is assumed constant, say 0) whereas in the solid and in the liquid regions u is negative or positive respectively and satisfies the corresponding heat conduction equation; the energy balance (Stefan condition) across the free boundary completes the model along with initial and boundary conditions.