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Algebra i Analiz, 2014, Volume 26, Issue 6, Pages 172–197 (Mi aa1412)  

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

Research Papers

On the proof of the solvability of a linear problem arising in magnetohydrodynamics with the method of integral equations

Sh. Sahaev, V. A. Solonnikov

St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka, 27, 191023, St. Petersburg, Russia

Abstract: The paper is concerned with a linear system of Fredholm–Volterra singular integral equations arising in the study of a linearized initial-boundary value problem of magnetohydrodymnamics for a fluid surrounded by an infinite vacuum region. It is proved that this system is solvable in the class of continuous functions satisfying the Hölder condition with respect to the spatial variables, which yields a classical solution of the problem in question.

Keywords: Fredholm–Volterra singular integral equations, classical solution.

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English version:
St. Petersburg Mathematical Journal, 2015, 26:6, 985–1003

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Received: 04.08.2014
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Citation: Sh. Sahaev, V. A. Solonnikov, “On the proof of the solvability of a linear problem arising in magnetohydrodynamics with the method of integral equations”, Algebra i Analiz, 26:6 (2014), 172–197; St. Petersburg Math. J., 26:6 (2015), 985–1003

Citation in format AMSBIB
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\jour Algebra i Analiz
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\issue 6
\pages 172--197
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Khompysh Kh., Sakhaev Sh.S., “on Estimates of Solutions of the Linear Stationary Problem of Magnetohydrodynamics Problem in Sobolev Spaces”, Advancements in Mathematical Sciences (Ams 2015), AIP Conference Proceedings, 1676, eds. Ashyralyev A., Malkowsky E., Lukashov A., Basar F., Amer Inst Physics, 2015, 020033  crossref  isi  scopus
    2. Sh. Sakhaev, “Estimates of a single problem of electrodynamics arising in magnetic hydrodynamics in space $W_{p}^{2,1} (Q_{T} ), p>1$”, Sib. elektron. matem. izv., 17 (2020), 1787–1796  mathnet  crossref
  • Алгебра и анализ St. Petersburg Mathematical Journal
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