Geodesic
A nonlocal problem for a~hyperbolic equation with integral conditions of the 1st kind with time-dependent kernels
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2012), pp. 32-44.

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

We consider a nonlocal problem with integral conditions of the 1st kind. The main goal is to prove the unique solvability of this problem under the assumption that kernels of nonlocal conditions depend both on spatial and time variables. To this end we propose a technique based on the proved equivalence between the nonlocal problem with integral conditions of the 1st kind and a nonlocal problem with integral conditions of the second kind in a special form. We formulate requirements to the initial data guaranteeing the unique existence of a generalized solution to the stated problem.
Keywords: hyperbolic equation, nonlocal problem, integral conditions, generalized solution. 
@article{IVM_2012_10_a2,
     author = {L. S. Pul'kina},
     title = {A nonlocal problem for a~hyperbolic equation with integral conditions of the 1st kind with time-dependent kernels},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {32--44},
     publisher = {mathdoc},
     number = {10},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2012_10_a2/}
}
TY  - JOUR
AU  - L. S. Pul'kina
TI  - A nonlocal problem for a~hyperbolic equation with integral conditions of the 1st kind with time-dependent kernels
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2012
SP  - 32
EP  - 44
IS  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2012_10_a2/
LA  - ru
ID  - IVM_2012_10_a2
ER  - 
%0 Journal Article
%A L. S. Pul'kina
%T A nonlocal problem for a~hyperbolic equation with integral conditions of the 1st kind with time-dependent kernels
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2012
%P 32-44
%N 10
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2012_10_a2/
%G ru
%F IVM_2012_10_a2
L. S. Pul'kina. A nonlocal problem for a~hyperbolic equation with integral conditions of the 1st kind with time-dependent kernels. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2012), pp. 32-44. http://geodesic.mathdoc.fr/item/IVM_2012_10_a2/

[1] Steklov V. A., “Zadacha ob okhlazhdenii neodnorodnogo tverdogo tela”, Soobsch. Kharkovskogo matem. o-va, 5:3–4 (1896), 136–181

[2] Dmitriev V. B., “Nelokalnaya zadacha s integralnymi usloviyami dlya volnovogo uravneniya”, Vestn. SamGU, 2006, no. 2(42), 15–27 | MR

[3] Lazhetich N. L., “O klassicheskoi razreshimosti smeshannoi zadachi dlya odnomernogo giperbolicheskogo uravneniya vtorogo poryadka”, Differents. uravneniya, 42:8 (2006), 1072–1077 | MR

[4] Kozhanov A. I., “O razreshimosti nekotorykh prostranstvenno nelokalnykh kraevykh zadach dlya lineinykh parabolicheskikh uravnenii”, Vestn. SamGU, 2008, no. 3(62), 165–174 | MR

[5] Pulkina L. S., Dyuzheva A. V., “Nelokalnaya zadacha s peremennymi po vremeni kraevymi usloviyami Steklova dlya giperbolicheskogo uravneniya”, Vestn. SamGU, 2010, no. 4(78), 56–64

[6] Kozhanov A. I., Pulkina L. S., “O razreshimosti nekotorykh granichnykh zadach so smescheniem dlya lineinykh giperbolicheskikh uravnenii”, Matem. zhurnal in-ta matem. (Almaty), 9:2(32) (2009), 78–92

[7] Pulkina L. S., “Kraevye zadachi dlya giperbolicheskogo uravneniya s nelokalnymi usloviyami 1 i 2-go roda”, Izv. vuzov. Matem., 2012, no. 4, 74–83

[8] Ladyzhenskaya O. A., Kraevye zadachi matematicheskoi fiziki, Nauka, M., 1973 | MR

[9] Evans L. K., Uravneniya s chastnymi proizvodnymi, Novosibirsk, 2003