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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
(published under the terms of the Creative Commons Attribution 4.0 International License)
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
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
Linking options:
https://www.mathnet.ru/eng/vsgtu1479 https://www.mathnet.ru/eng/vsgtu/v221/i1/p94
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