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Eurasian Mathematical Journal, 2021, Volume 12, Number 1, Pages 49–56
DOI: https://doi.org/10.32523/2077-9879-2021-12-1-49-56 (Mi emj391) 		 
This article is cited in 8 scientific papers (total in 8 papers)

One-phase spherical Stefan problem with temperature dependent coefficients

S. N. Kharinab, T. A. Nauryzbca

a Department of Mathematical and Computer Modeling, Institute of Mathematics and Mathematical Modeling, 125 Pushkin St, 050010 Almaty, Kazakhstan
b Kazakh-British Technical University, 59 Tole bi St, 050000 Almaty, Kazakhstan
c Al-Farabi Kazakh National University, 71/23 Al-Farabi St, 050040/A05E3B3 Almaty, Kazakhstan
Full-text PDF (365 kB) Citations (8)
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DOI: https://doi.org/10.32523/2077-9879-2021-12-1-49-56
Abstract: The one-phase spherical Stefan problem with coefficients depending on the temperature is considered. The method of solving is based on the similarity principle, which enables us to reduce this problem to a nonlinear ordinary differential equation, and then to an equivalent nonlinear integral equation of the Volterra type. It is shown that the obtained integral operator is a contraction operator and a unique solution exists.
Keywords and phrases: Stefan problem, nonlinear thermal coefficients, explicit solution, nonlinear integral equation, melting.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan AP09258948
The work is supported by the grant project AP09258948 of the Ministry of Education and Science of the Republic of Kazakhstan.
Received: 01.10.2020
Revised: 31.01.2021
Bibliographic databases:
Document Type: Article
MSC: 80A22, 35K05, 45D05
Language: English
Citation: S. N. Kharin, T. A. Nauryz, “One-phase spherical Stefan problem with temperature dependent coefficients”, Eurasian Math. J., 12:1 (2021), 49–56
Citation in format AMSBIB
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\by S.~N.~Kharin, T.~A.~Nauryz
\paper One-phase spherical Stefan problem with temperature dependent coefficients
\jour Eurasian Math. J.
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\vol 12
\issue 1
\pages 49--56
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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