Geodesic
A conditions of solvability of the Goursat problem in quadratures for the two-dimensional system of high order
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 21 (2017) no. 1, pp. 94-111

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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, solvability in quadratures.
Mots-clés : Goursat problem 
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     title = {A conditions of solvability of the {Goursat} problem in quadratures for the two-dimensional system of high order},
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E. A. Sozontova. A conditions of solvability of the Goursat problem in quadratures for the two-dimensional system of high order. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 21 (2017) no. 1, pp. 94-111. http://geodesic.mathdoc.fr/item/VSGTU_2017_21_1_a4/