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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.], 2017, Volume 21, Number 1, Pages 94–111 (Mi vsgtu1479)

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

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

DOI: https://doi.org/10.14498/vsgtu1479

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Bibliographic databases:

UDC: 517.956
MSC: 35K70
Revised: November 18, 2016
Accepted: December 9, 2016
First online: April 16, 2017

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{http://elibrary.ru/item.asp?id=29245099}