Geodesic
On solvability by quadratures conditions for second order hyperbolic systems
Ufa mathematical journal, Tome 8 (2016) no. 3, pp. 130-135

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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.
Keywords: hyperbolic system, boundary value problem, solvability by quadratures, factorization of equation.
Mots-clés : Goursat problem 
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     author = {E. A. Sozontova},
     title = {On solvability by quadratures conditions for second order hyperbolic systems},
     journal = {Ufa mathematical journal},
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     publisher = {mathdoc},
     volume = {8},
     number = {3},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UFA_2016_8_3_a11/}
}
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E. A. Sozontova. On solvability by quadratures conditions for second order hyperbolic systems. Ufa mathematical journal, Tome 8 (2016) no. 3, pp. 130-135. http://geodesic.mathdoc.fr/item/UFA_2016_8_3_a11/