Existence and uniqueness of strong solutions to the Stefan problem under weak assumptions on the input
Abstract
This work is a continuation of the research begun in [1]. The conditions for the smoothness of the input data are borderline between those for which the solution (statement) of the Stefan problem is weak (the statement does not include the equation for the phase-change boundary) and those for which it is strong, i.e. classical (the phases are separated by a smooth boundary). The strong global time solvability of the problem is established both in the case of an initial temperature close to the phase transition temperature and without this condition.
About the Author
A. G. Podgaev
Khabarovsk branch of the Institute of Applied Mathematics, Far Eastern Branch of the Russian Academy of Sciences
Russian Federation
Russian Federation
Aleksandr G. Podgaev
60 Seryshev Street, Khabarovsk 680038
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Review
For citations:
Podgaev A.G. Existence and uniqueness of strong solutions to the Stefan problem under weak assumptions on the input. Mathematical notes of NEFU. 2026;33(3):49-67. (In Russ.)
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