Geodesic
Nonlocal problem for degenerating hyperbolic equation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2017), pp. 50-56.

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We investigate a nonlocal problem for a degenerating hyperbolic equation in the domain, which is bounded by the characteristics of the equation. Boundary conditions include a linear combination of operators of fractional in the sense of Riemann-Liouville integrodifferentiation. The uniqueness of solution of the problem is proved by a modified Tricomi method. The existence is reduced to the equivalent of the solvability of a singular integral equation with Cauchy kernel or Fredholm integral equation of the second kind.
Keywords: nonlocal problem, operators of fractional integrodifferentiation, Cauchy problem, singular equation, Fredholm integral equation. 
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     author = {O. A. Repin and S. K. Kumykova},
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O. A. Repin; S. K. Kumykova. Nonlocal problem for degenerating hyperbolic equation. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2017), pp. 50-56. http://geodesic.mathdoc.fr/item/IVM_2017_7_a5/

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