Geodesic
Problem with nonlocal integral condition for pseudohyperbolic equation of the fourth-order
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 3 (2014), pp. 46-55 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this article, we study a problem for a multimensional pseudohyperbolic equation of the fourth-order with an integral condition. Existence and uniqueness of a generalized solution is proved.
Keywords: pseudohyperbolic equation, generalized solution, integral conditions. 
@article{VSGU_2014_3_a4,
     author = {S. V. Kirichenko},
     title = {Problem with nonlocal integral condition for pseudohyperbolic equation of the fourth-order},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {46--55},
     year = {2014},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2014_3_a4/}
}
TY  - JOUR
AU  - S. V. Kirichenko
TI  - Problem with nonlocal integral condition for pseudohyperbolic equation of the fourth-order
JO  - Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
PY  - 2014
SP  - 46
EP  - 55
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VSGU_2014_3_a4/
LA  - ru
ID  - VSGU_2014_3_a4
ER  - 
%0 Journal Article
%A S. V. Kirichenko
%T Problem with nonlocal integral condition for pseudohyperbolic equation of the fourth-order
%J Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
%D 2014
%P 46-55
%N 3
%U http://geodesic.mathdoc.fr/item/VSGU_2014_3_a4/
%G ru
%F VSGU_2014_3_a4
S. V. Kirichenko. Problem with nonlocal integral condition for pseudohyperbolic equation of the fourth-order. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 3 (2014), pp. 46-55. http://geodesic.mathdoc.fr/item/VSGU_2014_3_a4/

[1] Samarsky A. A., “On certain problems of modern theory of differential equations”, Differentsialnye uravneniya, 16:11 (1980), 1925–1935 | MR

[2] Gordeziani D. G., Avalishvili G. A., “Solutions of nonlocal problems for one-dimensional oscillations of the medium”, Matematicheskoe Modelirovanie, 12:1 (2000), 94–103 | MR | Zbl

[3] Bouziani A., Benouar N.-E., “Solution Forte d'un Problem Mixte avec Condition Non Locales pour une Classe d'equations Hyperboliques”, Bull. de la Classe des Sciences, Academie Royale de Belgique, 8 (1997), 53–70 | MR | Zbl

[4] Pulkina L. S., “Mixed problem with integral condition for the hyperbolic equation”, Mathematicheskie Zametki, 74:3 (2003), 411–421 | DOI | MR | Zbl

[5] Pulkina L. S., “Nonlocal problem with integral conditions for a hyperbolic equation”, Differentsialnye uravneniya, 40:7 (2004), 947–953 | MR | Zbl

[6] Kozhanov A. I., Pulkina L. S., “On the solvability of boundary value problems with nonlocal boundary condition of integral form for multidimentional hyperbolic equations”, Differentsialnye uravneniya, 42:9 (2006), 1233–1246 | MR | Zbl

[7] Pulkina L. S., “Initial-boundary value problem with a nonlocal boundary condition for a multidimensional hyperbolic equation”, Differentsialnye uravneniya, 44:8 (2008), 1084–1089 | MR | Zbl

[8] Pulkina L. S., “Boundary value problems for a hyperbolic equation with nonlocal conditions of the I and II kind”, Izvestiya VUZov, 2012, no. 4, 74–83 | MR | Zbl

[9] Pulkina L. S., “Nonlocal problem for a hyperbolic equation with integral conditions of the I-st kind with time-dependent kernels”, Izvestiya VUZov, 2012, no. 10, 32–44 | MR | Zbl

[10] Korpusov M. O., Blow-up in nonclassical wave equations, URSS, M., 2010, 237 pp.

[11] Ladyzhenskaya O. A., Boundary-value problems of mathematical physics, Nauka, M., 1973, 408 pp. | MR