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Ufimsk. Mat. Zh., 2016, Volume 8, Issue 3, Pages 135–140 (Mi ufa331)  

On solvability by quadratures conditions for second order hyperbolic systems

E. A. Sozontova

Elabuga Branch of Kazan (Volga Region) Federal University

Abstract: In the present work we consider boundary value problems for second order hyperbolic system with higher partial derivatives $u_{xy}$, $v_{xy}$ and $u_{xx}$, $v_{yy}$. The aim of the study is to find sufficient conditions for solvability of the considered problems by quadratures. We proposed a method for finding explicit solutions for the mentioned problems based on factorization of the equations in the original systems. As a result, in terms of the coefficients of these systems, we obtain 14 conditions for solvability by quadratures for each boundary value problem.

Keywords: hyperbolic system, Goursat problem, boundary value problem, solvability by quadratures, factorization of equation.

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English version:
Ufa Mathematical Journal, 2016, 8:3, 130–135 (PDF, 262 kB); https://doi.org/10.13108/2016-8-3-130

Bibliographic databases:

Document Type: Article
UDC: 517.956.3
MSC: 35L51, 35L53, 35G45
Received: 07.08.2015

Citation: E. A. Sozontova, “On solvability by quadratures conditions for second order hyperbolic systems”, Ufimsk. Mat. Zh., 8:3 (2016), 135–140; Ufa Math. J., 8:3 (2016), 130–135

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