Geodesic
Nonlocal problem with integral conditions for a system of hyperbolic equations in characteristic rectangle
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2017), pp. 11-25

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We consider a nonlocal problem with integral conditions for a system of hyperbolic equations in rectangular domain. We investigate the questions of existence of unique classical solution to the problem under consideration and approaches of its construction. Sufficient conditions of unique solvability to the investigated problem are established in the terms of initial data. The nonlocal problem with integral conditions is reduced to an equivalent problem consisting of the Goursat problem for the system of hyperbolic equations with functional parameters and functional relations. We propose algorithms for finding a solution to the equivalent problem with functional parameters on the characteristics and prove their convergence. We also obtain the conditions of a unique solvability to the boundary-value problem with integral condition for the system of an ordinary differential equations. As an example, we consider the nonlocal boundary-value problem with integral conditions for two-dimensional system of hyperbolic equations.
Keywords: system of hyperbolic equations, nonlocal problem, integral condition, solvability, algorithm. 
@article{IVM_2017_5_a1,
     author = {A. T. Assanova},
     title = {Nonlocal problem with integral conditions for a system of hyperbolic equations in characteristic rectangle},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {11--25},
     publisher = {mathdoc},
     number = {5},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_5_a1/}
}
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A. T. Assanova. Nonlocal problem with integral conditions for a system of hyperbolic equations in characteristic rectangle. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2017), pp. 11-25. http://geodesic.mathdoc.fr/item/IVM_2017_5_a1/