Abstract
The existence of the classical solution of the many-dimensional two-phase Stefan problem is proved for any finite time interval in the case of contact of an unknown (free) boundary with the known one.
Similar content being viewed by others
References
A. Fridman,Variation Principles and Problems with Free Boundaries [in Russian], Nauka, Moscow (1990).
I. I. Danilyuk, “On the Stefan problem,”Usp. Mat.Nauk,40, No. 5, 133–185 (1985).
B. V. Bazalii, “The Stefan problem,”Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 11, 3–7 (1986).
A. M. Meirmanov,The Stefan Problem [in Russian], Nauka, Novosibirsk (1986).
E. V. Radkevich and A. K. Melikulov,Boundary-Value Problems with Free Boundary [in Russian], Fan, Tashkent (1988).
M. A. Borodin, “On the solvability of the two-phase nonstationary Stefan problem,”Dokl. Akad. Nauk SSSR,263, No. 5, 1040–1042 (1982).
M. A. Borodin, “Existence of the classical solution of a many-dimensional two-phase Stefan problem on any finite time interval,”Intern. Ser. Numer. Math.,106, 97–103 (1992).
O. A. Ladyzhenskaya and N. N. Ural'tseva,Linear and Quasilinear Equations of Elliptic Type [in Russian], Nauka, Moscow (1973).
E. V. Radkevich, “On the spectrum of the bundle of the two-phase Stefan problem,”Dokl. Akad. Nauk SSSR,314, No. 6, 1322–1327 (1990).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 2, pp. 158–167, February, 1995.
Rights and permissions
About this article
Cite this article
Borodin, M.A. Two-phase contact Stefan problem. Ukr Math J 47, 187–198 (1995). https://doi.org/10.1007/BF01056709
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01056709