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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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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2017, Volume 21, Number 1, Pages 94–111
DOI: https://doi.org/10.14498/vsgtu1479 (Mi vsgtu1479) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Differential Equations and Mathematical Physics

A conditions of solvability of the Goursat problem in quadratures for the two-dimensional system of high order

E. A. Sozontova

Elabuga Branch of Kazan (Volga Region) Federal University, Elabuga, 423600, Russian Federation
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DOI: https://doi.org/10.14498/vsgtu1479
Abstract: In this paper we consider the Goursat problem for the two-dimensional system of high order. The purpose is to find sufficient conditions of solvability of the considered problem in quadratures. The method of finding solutions of these problems in explicit calculation based on factorization of equations is devised. As a result the initial problem is reduced to 5 simpler problems: to four Goursat problems for equation and the Goursat problem for hyperbolic system of the second order. The final result in terms of the coefficients of the original system is formulated in two theorems.
Keywords: system of differential equations, Goursat problem, solvability in quadratures.
Received: March 6, 2016
Revised: November 18, 2016
Accepted: December 9, 2016
First online: April 16, 2017
Bibliographic databases:
Document Type: Article
UDC: 517.956
MSC: 35K70
Language: Russian
Citation: E. A. Sozontova, “A conditions of solvability of the Goursat problem in quadratures for the two-dimensional system of high order”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 21:1 (2017), 94–111
Citation in format AMSBIB
\Bibitem{Soz17}
\by E.~A.~Sozontova
\paper A conditions of solvability of the Goursat problem in quadratures for the two-dimensional system of high order
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2017
\vol 21
\issue 1
\pages 94--111
\mathnet{http://mi.mathnet.ru/vsgtu1479}
\crossref{https://doi.org/10.14498/vsgtu1479}
\elib{https://elibrary.ru/item.asp?id=29245099}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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