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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2018, Volume 149, Pages 14–24 (Mi into313)  
This article is cited in 3 scientific papers (total in 3 papers)

Nonlocal Boundary-Value Problem for a Third-Order Equation of Parabolic-Hyperbolic Type with Degeneration of Type and Order in the Hyperbolicity Domain

Zh. A. Balkizov

Institute of Applied Mathematics and Automation, Nalchik
Full-text PDF (215 kB) Citations (3)
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Abstract: We consider a nonlocal boundary-value problem for a third-order parabolic-hyperbolic equation with degeneracy of type and order in the domain of hyperbolicity, containing second-order derivatives in the boundary conditions. Sufficient conditions of the unique solvability of the problem are obtained. The Tricomi method is used to prove the uniqueness theorem for a solution. The solution of the problem is expressed in the explicit form.
Keywords: degenerate hyperbolic equation of the first kind, equation with multiple characteristics, third-order parabolic-hyperbolic equation, mixed boundary-value problem, nonlocal boundary-value problem, Tricomi problem, Tricomi method, Volterra integral equation of the second kind, Fredholm integral equation of the second kind.
English version:
Journal of Mathematical Sciences (New York), 2020, Volume 250, Issue 5, Pages 728–739
DOI: https://doi.org/10.1007/s10958-020-05037-z
Bibliographic databases:
Document Type: Article
UDC: 517.956.6
MSC: 35M10, 35M13
Language: Russian
Citation: Zh. A. Balkizov, “Nonlocal Boundary-Value Problem for a Third-Order Equation of Parabolic-Hyperbolic Type with Degeneration of Type and Order in the Hyperbolicity Domain”, Proceedings of the International Conference “Actual Problems of Applied Mathematics and Physics,” Kabardino-Balkaria, Nalchik, May 17–21, 2017, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 149, VINITI, Moscow, 2018, 14–24; J. Math. Sci. (N. Y.), 250:5 (2020), 728–739
Citation in format AMSBIB
\Bibitem{Bal18}
\by Zh.~A.~Balkizov
\paper Nonlocal Boundary-Value Problem for a Third-Order Equation of Parabolic-Hyperbolic Type with Degeneration of Type and Order in the Hyperbolicity Domain
\inbook Proceedings of the International Conference ``Actual Problems of Applied Mathematics and Physics,'' Kabardino-Balkaria, Nalchik, May 17--21, 2017
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2018
\vol 149
\pages 14--24
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into313}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3847719}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2020
\vol 250
\issue 5
\pages 728--739
\crossref{https://doi.org/10.1007/s10958-020-05037-z}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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