Abstract:
In the present work we consider boundary value problems for second order hyperbolic system with higher partial derivatives uxy, vxy and uxx, vyy. 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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