Bizhanova, G. I. 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 \(\alpha(t)=\alpha_0\sqrt{t}\). Reviewer: Nikolai V. Krasnoschok (Donetsk) Cited in 1 Document MSC: 35R35 Free boundary problems for PDEs 35K20 Initial-boundary value problems for second-order parabolic equations 80A22 Stefan problems, phase changes, etc. Keywords:exact solutions; Stefan problem; Verigin problem; Florin problem PDFBibTeX XMLCite \textit{G. I. Bizhanova}, Zap. Nauchn. Semin. POMI 318, 42--59 (2004; Zbl 1082.35164); translation in J. Math. Sci., New York 136, No. 2, 3672--3681 (2006) Full Text: EuDML