Analytic solution of the Stefan problem in finite mediums. (English) Zbl 0810.35164
Summary: The classical Stefan problem is considered in this paper for finite mediums with Dirichlet boundary conditions. Analytic solutions for the temperature distributions and the location of the moving interface are obtained by using Lie group theory and the superposition principle. The existence of analytically exact solutions is established by proving the convergence of the solution.
MSC:
35R35 | Free boundary problems for PDEs |
35K05 | Heat equation |
22E70 | Applications of Lie groups to the sciences; explicit representations |
80A22 | Stefan problems, phase changes, etc. |