Investigation of solvability of the Stefan problem for the case of complex structure of matter
https://doi.org/10.25587/2411-9326-2025-3-61-81
Abstract
Using compactness methods for functions from the scale of Banach spaces, we prove the solvability of the problem with nonlinear latent heat of matter fusion in Stefan’s condition. An initial boundary value problem in a non-cylindrical domain with a given curved boundary of class W1/2 is preliminarily investigated, for which we obtain uniform estimates necessary for the main problem. Then we consider a problem in which the coefficient of the latent specific heat of fusion in the condition on the unknown boundary is a function of the size of the thawing zone s(t). This technique can also be applied to more general equations. The studied problem describes the processes of transition of matter from one state to another. As a result, the regular global in time solvability of the one-phase Stefan problem for the nonlinear parabolic equation is established. The initial data belong only to the class W1/2, while the phase transition boundary defined together with the solution belongs to W1/4.
About the Authors
A. G. Podgaev
Khabarovsk branch of the Institute of Applied Mathematics, Far Eastern Branch of the Russian Academy of Sciences;
Pacific State University
Russian Federation
Russian Federation
Aleksandr G. Podgaev
60 Seryshev Street, Khabarovsk 680038
136 Tikhookeanskaya Street, Khabarovsk 680035
T. D. Kulesh
Pacific State University
Russian Federation
Russian Federation
Timofey D. Kulesh
136 Tikhookeanskaya Street, Khabarovsk 680035
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Review
For citations:
Podgaev A.G., Kulesh T.D. Investigation of solvability of the Stefan problem for the case of complex structure of matter. Mathematical notes of NEFU. 2025;32(3):61-81. (In Russ.) https://doi.org/10.25587/2411-9326-2025-3-61-81
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