Geodesic
On exact solutions of one-dimensional two phase free boundary problems for parabolic equations
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 36, Tome 318 (2004), pp. 42-59 
G. I. Bizhanova. On exact solutions of one-dimensional two phase free boundary problems for parabolic equations. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 36, Tome 318 (2004), pp. 42-59. http://geodesic.mathdoc.fr/item/ZNSL_2004_318_a2/
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     author = {G. I. Bizhanova},
     title = {On exact solutions of one-dimensional two phase free boundary problems for parabolic equations},
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     year = {2004},
     volume = {318},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2004_318_a2/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The paper is concerned with auto-modelling solutions of one-dimensional two phase Stefan, Florin, and Verigin free boundary problems for parabolic equations whose initial and boundary data are not adjusted. It is shown that in the Stefan problem with “supercooling” a liquid can have a temperature less than the temperature of the phase transition, i.e., a liqued can be “supercooled” and solid “superheated.”

[1] L. I. Rubinshtein, Problema Stefana, Zvaigzne, Riga, 1967 | MR

[2] A. N. Tikhonov, A. A. Samarskii, Uravneniya matematicheskoi fiziki, Nauka, M., 1972 | MR

[3] N. N. Verigin, “Nagnetanie vyazhuschikh rastvorov v gornye porody v usloviyakh povysheniya prochnosti i nepronitsaemosti osnovanii gidrotekhnicheskikh sooruzhenii”, Izvestiya AN SSSR, 1952, no. 5, 674–687

[4] V. A. Florin, “Uplotnenie zemlyanoi sredy i filtratsiya pri peremennoi poristosti s uchetom vliyaniya svyazannoi vody”, Izvestiya AN SSSR. OTN, 1951, no. 1, 1625–1649

[5] A. Fridman, B. Hu, “The Stefan problem with kinetic condition at the free boundary”, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 19:1 (1992), 87–111 | MR

[6] I. G. Gëtts, A. M. Meirmanov, “Obobschennoe reshenie zadachi Stefana s kineticheskim pereokhlazhdeniem”, Sibirskii zhurnal industrialnoi matematiki, 3:1 (2000), 66–86 | MR | Zbl

[7] G. I. Bizhanova, A. Sarsekeeva, “On the solvability of free boundary problems with supercooling”, Far East Journal of Applied Mathematics, 15:2 (2004), 223–243 | MR | Zbl

[8] M. Abramovets, I. Stigan (red.), Spravochnik po spetsialnym funktsiyam, Nauka, M., 1979 | MR