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.
\Bibitem{Soz16}
\by E.~A.~Sozontova
\paper On solvability by quadratures conditions for second order hyperbolic systems
\jour Ufa Math. J.
\yr 2016
\vol 8
\issue 3
\pages 130--135
\mathnet{http://mi.mathnet.ru/eng/ufa331}
\crossref{https://doi.org/10.13108/2016-8-3-130}
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Linking options:
https://www.mathnet.ru/eng/ufa331
https://doi.org/10.13108/2016-8-3-130
https://www.mathnet.ru/eng/ufa/v8/i3/p135
This publication is cited in the following 1 articles:
E. A. Sozontova, “Usloviya suschestvovaniya i edinstvennosti resheniya zadachi Gursa dlya sistemy uravnenii s dominiruyuschimi chastnymi proizvodnymi”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 27:2 (2023), 375–383
Citation in format AMSBIB
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