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 Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]: Year: Volume: Issue: Page: Find

 Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2019, Volume 23, Number 1, Pages 186–194 (Mi vsgtu1666)

Short Communication

The Goursat-type problem for a hyperbolic equation and system of third order hyperbolic equations

A. A. Andreev, J. O. Yakovleva*

Samara State Technical University, Samara, 443100, Russian Federation

Abstract: In the first part of this study, the well-posed Goursat-type problem is considered for the hyperbolic differential equation of the third order with non-multiple characteristics. The example illustrating the non-well-posed Goursat-type problem for the hyperbolic differential equation of the third order is discussed. The regular solution of the Goursat-type problem for the hyperbolic differential equation of the third order with the non-multiple characteristics is obtained in an explicit form.
In the second part, the well-posed Goursat-type problem is considered for a system of the hyperbolic differential equations of the third order. The regular solution of the Goursat-type problem for this system is also obtained in an explicit form.
The theorems for the Hadamard's well-posedness of Goursat-type problem for the hyperbolic differential equation and for a system of the hyperbolic differential equations is formulated as the result of the research.

Keywords: third order hyperbolic equation, non-multiple characteristics, Goursat-type problem, hyperbolic system of third order differential equations, Hadamard correctness
* Author to whom correspondence should be addressed

DOI: https://doi.org/10.14498/vsgtu1666

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Bibliographic databases:

UDC: 517.956.3
MSC: 74E35, 74K20
Revised: February 14, 2019
Accepted: March 4, 2019
First online: March 25, 2019

Citation: A. A. Andreev, J. O. Yakovleva, “The Goursat-type problem for a hyperbolic equation and system of third order hyperbolic equations”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 23:1 (2019), 186–194

Citation in format AMSBIB
\Bibitem{AndYak19} \by A.~A.~Andreev, J.~O.~Yakovleva \paper The Goursat-type problem for a hyperbolic equation and~system of third order hyperbolic equations \jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.] \yr 2019 \vol 23 \issue 1 \pages 186--194 \mathnet{http://mi.mathnet.ru/vsgtu1666} \crossref{https://doi.org/10.14498/vsgtu1666} \zmath{https://zbmath.org/?q=an:07097288} \elib{https://elibrary.ru/item.asp?id=37248567} 

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