On a One-Phase Stefan Problem in Nonlinear Conduction
نویسنده
چکیده
One and two phase Stefan problems for the linear heat equation have been the subject of many studies in the past [1, 2]. Indeed these problems have a great physical relevance since they provide a mathematical model for the processes of phase changes [3, 4]. The boundary between the two phases is a free boundary: its motion has to be determined as part of the solution. More recently the previous analysis was extended to nonlinear diffusion models. In [5, 6] exact solutions were found in parametric form for a class of Stefan problems in nonlinear heat conduction. Moreover one and two-phase Stefan problems for the Burgers equation were solved in [7, 8] and explicit travelling wave solutions were obtained. It is the aim of this paper to formulate and solve a one-phase Stefan problem for the nonlinear heat equation:
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