Geodesic
Nonlocal problem with integral condition for a fourth order equation
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 10 (2014), pp. 26-37 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper, we consider a nonlocal problem with integral condition with respect to spacial variable for a forth order partial differential equation. The conditions on the data for unique solvability of the problem in Sobolev space are determined. Proving of uniqueness of generalized solution is based on acquired apriori estimates. To prove the solvability we use a following scheme: sequence of approximate solutions using Galerkin procedure is built, apriory estimates that allow to extract from it a convergent subsequence are received, on the final stage it is shown that the limit of subsequence is the required generalized solution.
Keywords: nonlocal problem, integral condition, Sobolev space, generalized solution, solubility. 
@article{VSGU_2014_10_a2,
     author = {N. V. Beilina},
     title = {Nonlocal problem with integral condition for a fourth order equation},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {26--37},
     year = {2014},
     number = {10},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2014_10_a2/}
}
TY  - JOUR
AU  - N. V. Beilina
TI  - Nonlocal problem with integral condition for a fourth order equation
JO  - Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
PY  - 2014
SP  - 26
EP  - 37
IS  - 10
UR  - http://geodesic.mathdoc.fr/item/VSGU_2014_10_a2/
LA  - ru
ID  - VSGU_2014_10_a2
ER  - 
%0 Journal Article
%A N. V. Beilina
%T Nonlocal problem with integral condition for a fourth order equation
%J Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
%D 2014
%P 26-37
%N 10
%U http://geodesic.mathdoc.fr/item/VSGU_2014_10_a2/
%G ru
%F VSGU_2014_10_a2
N. V. Beilina. Nonlocal problem with integral condition for a fourth order equation. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 10 (2014), pp. 26-37. http://geodesic.mathdoc.fr/item/VSGU_2014_10_a2/

[1] Pulkina L. S., Problems with nonclassical conditions for hyperbolic equations, Izd-vo “Samarskii universitet”, Samara, 2012 (in Russian)

[2] Avalishvili G., Avalishvili M., Gordeziani D., “On Integral Nonlocal Boundary Value Problems for some Partial Differential Equations”, Bulletin of the Georgian National Academy of Sciences, 5:1 (2011), 31–37 | MR | Zbl

[3] Ashyralyev A., Aggez N., “On the Solution of Multipoint NBVP for Hyperbolic Equation with Integral Condition”, Malaysian Journal of Mathematical Sciences, 2012, no. 6(S), 111–121 | MR

[4] Beilin S. A., “Mixed problem with integral condition for the wave equation”, Nonclassical equations of mathematical physics, Izd-vo In-ta matematiki, Novosibirsk, 2005, 37–43 (in Russian)

[5] Bouziani A., “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, 1997, no. 8, 53–70 | MR | Zbl

[6] Beilina N. V., “On solvability of a problem with integral condition for multidimensinal hyperbolic equation”, Vestnik SamSU. Natural Science Series, 2010, no. 2(78), 12–20 (in Russian)

[7] Pul'kina L. S., “Boundary-value problem for a hyperbolic equation with nonlocal conditions of the I and II kind”, News of Higher Educational Institutions. Mathematics, 2012, no. 4, 74–83 (in Russian)

[8] Pul'kina L. S., “A nonlocal problem for a hyperbolic equation with integral conditions of the 1st kind with time-depended kernels”, News of Higher Educational Institutions. Mathematics, 2012, no. 10, 32–44 (in Russian)

[9] Tikhonov A. N., Samarskii A. A., Equations of mathematical physics, 5th ed., Nauka, M., 1977 (in Russian)

[10] Krylov A. N., Vibration of vessels, Department of Scientific and Technical Information of NKTP. Redaktsiia sudostroitel'noi literatury, L.–M., 1936 (in Russian)

[11] Ladyzhenskaya O. A., Boundary problems of mathematical physics, Nauka, M., 1973 (in Russian) | MR

[12] Garding L., Gauchy's problem for hyperbolic equations, IL, M., 1961 (in Russian)

[13] Beilina N. V., “A nonlocal problem with integral condition for pseudohyperbolic equation”, Vestnik SamSU. Natural Science Series, 2008, no. 2(61), 22–28 (in Russian)