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Dal'nevost. Mat. Zh., 2021, Volume 21, Number 1, Pages 105–112 (Mi dvmg450)  

Compactness theorems for problems with unknown boundary

A. G. Podgaev, T. D. Kulesh

Pacific National University, Khabarovsk

Abstract: The compactness theorem is proved for sequences of functions that have estimates of the higher derivatives in each subdomain of the domain of definition, divided into parts by a sequence of some curves of class $W_2^1$. At the same time, in the entire domain of determining summable higher derivatives, these sequences do not have. These results allow us to make limit transitions using approximate solutions in problems with an unknown boundary that describe the processes of phase transitions.

Key words: Stefan's problems, quasilinear parabolic equation, non-cylindrical domain, compactness theorem.

Funding Agency Grant Number
Ministry of Science and Higher Education of the Russian Federation 075-02-2020-1529/1


DOI: https://doi.org/10.47910/FEMJ202109

Full text: PDF file (506 kB)
References: PDF file   HTML file

UDC: 517.957
MSC: Primary 80A22; Secondary 35K55, 46N20
Received: 28.03.2021

Citation: A. G. Podgaev, T. D. Kulesh, “Compactness theorems for problems with unknown boundary”, Dal'nevost. Mat. Zh., 21:1 (2021), 105–112

Citation in format AMSBIB
\Bibitem{PodKul21}
\by A.~G.~Podgaev, T.~D.~Kulesh
\paper Compactness theorems for problems with unknown boundary
\jour Dal'nevost. Mat. Zh.
\yr 2021
\vol 21
\issue 1
\pages 105--112
\mathnet{http://mi.mathnet.ru/dvmg450}
\crossref{https://doi.org/10.47910/FEMJ202109}


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