Article
Ufa Mathematical Journal
Volume 8, Number 3, pp. 130-135
On solvability by quadratures conditions for second order hyperbolic systems
Sozontova E.A.
DOI:10.13108/2016-8-3-130
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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.