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This article is cited in 1 scientific paper (total in 1 paper)
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.
Received: 07.08.2015
Citation:
E. A. Sozontova, “On solvability by quadratures conditions for second order hyperbolic systems”, Ufa Math. J., 8:3 (2016), 130–135
Linking options:
https://www.mathnet.ru/eng/ufa331https://doi.org/10.13108/2016-8-3-130 https://www.mathnet.ru/eng/ufa/v8/i3/p135
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