Geodesic
A problem with nonlocal initial data for one-dimensional hyperbolic equation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2014), pp. 17-26.

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

In this article we consider a boundary-value problem for hyperbolic equation with nonlocal initial data in integral form. We prove the existence and uniqueness of generalized solution.
Keywords: hyperbolic equation, nonlocal problem, integral conditions, generalized solution. 
@article{IVM_2014_9_a1,
     author = {S. V. Kirichenko and L. S. Pul'kina},
     title = {A problem with nonlocal initial data for one-dimensional hyperbolic equation},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {17--26},
     publisher = {mathdoc},
     number = {9},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2014_9_a1/}
}
TY  - JOUR
AU  - S. V. Kirichenko
AU  - L. S. Pul'kina
TI  - A problem with nonlocal initial data for one-dimensional hyperbolic equation
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2014
SP  - 17
EP  - 26
IS  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2014_9_a1/
LA  - ru
ID  - IVM_2014_9_a1
ER  - 
%0 Journal Article
%A S. V. Kirichenko
%A L. S. Pul'kina
%T A problem with nonlocal initial data for one-dimensional hyperbolic equation
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2014
%P 17-26
%N 9
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2014_9_a1/
%G ru
%F IVM_2014_9_a1
S. V. Kirichenko; L. S. Pul'kina. A problem with nonlocal initial data for one-dimensional hyperbolic equation. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2014), pp. 17-26. http://geodesic.mathdoc.fr/item/IVM_2014_9_a1/

[1] Samarskii A. A., “O nekotorykh problemakh sovremennoi teorii differentsialnykh uravnenii”, Differents. uravneniya, 16:11 (1980), 1925–1935 | MR

[2] Cannon J. R., “The solution of the heat equation subject to the specification of energy”, Quart. Appl. Math., 21:1 (1963), 155–160 | MR

[3] Gordeziani D. G., Avalishvili G. A., “Resheniya nelokalnykh zadach dlya odnomernykh kolebanii sredy”, Matem. modelir., 12:1 (2000), 94–103 | MR | Zbl

[4] Kozhanov A. I., Pulkina L. S., “O razreshimosti kraevykh zadach s nelokalnym granichnym usloviem integralnogo vida dlya mnogomernykh giperbolicheskikh uravnenii”, Differents. uravneniya, 42:9 (2006), 1166–1179 | MR | Zbl

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

[6] Pulkina L. S., “Nelokalnaya zadacha dlya giperbolicheskogo uravneniya s integralnymi usloviyami I roda s yadrami, zavisyaschimi ot vremeni”, Izv. vuzov. Matem., 2012, no. 10, 32–44 | MR

[7] Kuz A. M., Ptashnik B. I., “Zadacha z integralnimi umovami dlya rivnyannya Kleina–Gordona u klassi funktsii, maizhe periodichnikh za prostorovimi zminnimi”, Prikl. problemi mekh. i mat., 2010, no. 8, 41–53

[8] Abdrakhmanov A. M., Kozhanov A. I., “Zadacha s nelokalnym granichnym usloviem dlya odnogo klassa uravnenii nechetnogo poryadka”, Izv. vuzov. Matem., 2007, no. 5, 3–12 | MR | Zbl

[9] Lukina G. A., “Kraevye zadachi s integralnymi granichnymi usloviyami po vremeni dlya uravnenii tretego poryadka”, Matem. zametki YaGU, 17:2 (2010), 75–97 | Zbl

[10] Prilepko A. I., Kostin A. B., “O nekotorykh obratnykh zadachakh dlya parabolicheskikh uravnenii s finalnym i integralnym pereopredeleniem”, Matem. sb., 183:4 (1992), 49–68 | MR | Zbl

[11] Cannon J. R., Lin Y. P., “An inverse problem of finding a parameter in a semi-linear heat equation”, J. Math. Anal. Appl., 145:2 (1990), 470–484 | DOI | MR | Zbl

[12] Kamynin V. L., Kostin A. B., “Dve obratnye zadachi opredeleniya koeffitsienta v parabolicheskom uravnenii”, Differents. uravneniya, 46:3 (2010), 372–383 | MR | Zbl

[13] Denisov A. M., Vvedenie v teoriyu obratnykh zadach, Izd-vo Mosk. un-ta, M., 1994

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