Geodesic
A mixed problem with nonlinear integral condition for a hyperbolic equation
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 6 (2009), pp. 35-49 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Mixed problem for the hyperbolic equation with non-linear integral condition instead of a standard boundary condition and non-linear right side is viewed in the work. The task is viewed in the space of arbitrary dimensionality. The existence and uniqueness of the solution is proved.
Keywords: nonlocal problem, hyperbolic equation, generalized solution.
Mots-clés : apriori estimation 
@article{VSGU_2009_6_a3,
     author = {V. B. Dmitriev},
     title = {A mixed problem with nonlinear integral condition for a~hyperbolic equation},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {35--49},
     year = {2009},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2009_6_a3/}
}
TY  - JOUR
AU  - V. B. Dmitriev
TI  - A mixed problem with nonlinear integral condition for a hyperbolic equation
JO  - Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
PY  - 2009
SP  - 35
EP  - 49
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/VSGU_2009_6_a3/
LA  - ru
ID  - VSGU_2009_6_a3
ER  - 
%0 Journal Article
%A V. B. Dmitriev
%T A mixed problem with nonlinear integral condition for a hyperbolic equation
%J Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
%D 2009
%P 35-49
%N 6
%U http://geodesic.mathdoc.fr/item/VSGU_2009_6_a3/
%G ru
%F VSGU_2009_6_a3
V. B. Dmitriev. A mixed problem with nonlinear integral condition for a hyperbolic equation. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 6 (2009), pp. 35-49. http://geodesic.mathdoc.fr/item/VSGU_2009_6_a3/

[1] Gording L., Zadacha Koshi dlya giperbolicheskikh uravnenii, Inostr. lit., M., 1961, 122 pp.

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

[3] Dmitriev V. B., “Nelokalnaya zadacha s integralnym usloviem dlya uravneniya giperbolicheskogo tipa”, Vestn. Sam. gos. tekhn. un-ta. Ser.: Fiz.-mat. nauki, 2006, no. 42, 35–40

[4] Kozhanov A. I., Pulkina L. S., “O razreshimosti kraevykh zadach s nelokalnym granichnym usloviem integralnogo vida dlya mnogomernykh giperbolicheskikh uravnenii”, Doklady Akademii nauk, 404:5 (2005) | MR | Zbl

[5] Ladyzhenskaya O. A., Kraevye zadachi matematicheskoi fiziki, Nauka, M., 1973, 408 pp. | MR

[6] Ladyzhenskaya O. A., Solonnikov V. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967, 736 pp. | MR

[7] Pontryagin L. S., Obyknovennye differentsialnye uravneniya: uchebnik dlya un-tov, izd. 4-e, Nauka, M., 1974, 331 pp.