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Abstract
WE consider the solution of a two-phase Stefan problem for a quasilinear parabolic equation by the method of straight lines. We describe the method and prove the existence and uniqueness of the solution under fairly weak restrictions on the initial data. The Stefan problem is well known to describe only to a first approximation processes with a moving boundary of separation, since an advance of the front leads to mass transport. The latter is determined by the dynamics of the temperature field and in turn considerably influences the velocity of motion of the front. It is very difficult to use the familiar methods for solving Stefan's problem [1–7] when heat and mass exchange occur. Some variants of the method of straight lines when the front is moving monotonically are considered in [5, 8, 9]. The method described below for solving the Stefan's problem involving explicit determination of the front can easily be extended to the “systemic” case just mentioned. An application of the method of straight lines to a concrete problem of heat and mass exchange, describing the migration of moisture to a freezing front, allowing for swelling, will form the topic of a special study.
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