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On exact solutions of one-dimensional diffusion problems with free boundaries for parabolic equations. (Russian, English) Zbl 1082.35164

Zap. Nauchn. Semin. POMI 318, 42-59 (2004); translation in J. Math. Sci., New York 136, No. 2, 3672-3681 (2006).
This paper is devoted to the construction of exact solutions to one-dimensional two-phase free boundary problems of various types: Stefan problem, Verigin problem and Florin problem, under different assumptions on initial data. The free boundary \(\alpha(t)\) has in all cases the form \(\alpha(t)=\alpha_0\sqrt{t}\).

MSC:

35R35 Free boundary problems for PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
80A22 Stefan problems, phase changes, etc.
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