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Contemporary Mathematics. Fundamental Directions, 2023, Volume 69, Issue 4, Pages 676–684
DOI: https://doi.org/10.22363/2413-3639-2023-69-4-676-684
(Mi cmfd521)
 

This article is cited in 2 scientific papers (total in 2 papers)

On the structure of weak solutions of the Riemann problem for a degenerate nonlinear diffusion equation

E. Yu. Panovab

a Research and Development Center, Novgorod the Great, Russia
b Yaroslav-the-Wise Novgorod State University, Novgorod the Great, Russia
Full-text PDF (246 kB) Citations (2)
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Abstract: An explicit form of weak solutions to the Riemann problem for a degenerate nonlinear parabolic equation with a piecewise constant diffusion coefficient is found. It is shown that the lines of phase transitions (free boundaries) correspond to the minimum point of some strictly convex and coercive function of a finite number of variables. A similar result is true for Stefan's problem. In the limit, when the number of phases tends to infinity, there arises a variational formulation of self-similar solutions to the equation with an arbitrary nonnegative diffusion function.
Keywords: degenerate nonlinear parabolic equation, Riemann problem, Stefan problem, weak solution, phase transition, self-similar solution.
Funding agency Grant number
Russian Science Foundation 22-21-00344
The work was supported by the Russian Science Foundation, grant No. 22-21-00344.
Bibliographic databases:
Document Type: Article
UDC: 517.957
Language: Russian
Citation: E. Yu. Panov, “On the structure of weak solutions of the Riemann problem for a degenerate nonlinear diffusion equation”, CMFD, 69, no. 4, PFUR, M., 2023, 676–684
Citation in format AMSBIB
\Bibitem{Pan23}
\by E.~Yu.~Panov
\paper On the structure of weak solutions of the Riemann problem for a degenerate nonlinear diffusion equation
\serial CMFD
\yr 2023
\vol 69
\issue 4
\pages 676--684
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd521}
\crossref{https://doi.org/10.22363/2413-3639-2023-69-4-676-684}
\edn{https://elibrary.ru/ZEGDSE}
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Современная математика. Фундаментальные направления
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