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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{IVM_2017_7_a5,
     author = {O. A. Repin and S. K. Kumykova},
     title = {Nonlocal problem for degenerating hyperbolic equation},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {50--56},
     publisher = {mathdoc},
     number = {7},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_7_a5/}
}
TY  - JOUR
AU  - O. A. Repin
AU  - S. K. Kumykova
TI  - Nonlocal problem for degenerating hyperbolic equation
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2017
SP  - 50
EP  - 56
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2017_7_a5/
LA  - ru
ID  - IVM_2017_7_a5
ER  - 
%0 Journal Article
%A O. A. Repin
%A S. K. Kumykova
%T Nonlocal problem for degenerating hyperbolic equation
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2017
%P 50-56
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2017_7_a5/
%G ru
%F IVM_2017_7_a5
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/