The Classical Stefan Problem as the Limit Case of the Stefan Problem with a Kinetic Condition at the Free Boundary

Abstract

In some papers mathematical models of solidification have been grounded as the limit of the boundary problems of the phase-field equations (see e.g. []). At the same time with the classical Stefan problem, which contains a constant-temperature condition at the interface (this temperature is an equilibrium melting temperature), there arises a modified Stefan problem, in which the phase-change temperature depends on the velocity and curvature of the interface (classical Stefan condition is replaced by the kinetic condition).