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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2020, Volume 24, Number 2, Pages 211–225 (Mi vsgtu1694)  

Differential Equations and Mathematical Physics

On a boundary value problem for a third-order parabolic-hyperbolic type equation with a displacement boundary condition in its hyperbolicity domain

Zh. A. Balkizov

Institute of Applied Mathematics and Automation of Kabardin-Balkar Scientific Centre of RAS, Nal'chik, 360000, Russian Federation

Abstract: In the article, we investigate a boundary-value problem with a third-order inhomogeneous parabolic-hyperbolic equation with a wave operator in a hyperbolicity domain. A linear combination with variable coefficients in terms of derivatives of the sought function on independent characteristics, as well as on the line of type and order changing is specified as a boundary condition. We have established necessary and sufficient conditions that guarantee existence and uniqueness of a regular solution to the problem under study. In some cases, a solution representation is written out explicitly.

Keywords: degenerate hyperbolic equation, equation with multiple characteristics, parabolic-hyperbolic equation of third order, problems with a shift

DOI: https://doi.org/10.14498/vsgtu1694

Full text: PDF file (962 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 517.956.6
MSC: 35M12, 35M32
Received: April 24, 2019
Revised: November 19, 2019
Accepted: January 27, 2020
First online: May 27, 2020
Language:

Citation: Zh. A. Balkizov, “On a boundary value problem for a third-order parabolic-hyperbolic type equation with a displacement boundary condition in its hyperbolicity domain”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 24:2 (2020), 211–225

Citation in format AMSBIB
\Bibitem{Bal20}
\by Zh.~A.~Balkizov
\paper On a boundary value problem for a third-order parabolic-hyperbolic type equation
with a displacement boundary condition in its hyperbolicity domain
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2020
\vol 24
\issue 2
\pages 211--225
\mathnet{http://mi.mathnet.ru/vsgtu1694}
\crossref{https://doi.org/10.14498/vsgtu1694}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000555617100001}


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  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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