Geodesic
Inverse boundary value problem for a Boussinesq type equation of fourth order with nonlocal time integral conditions of the second kind
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 26 (2016) no. 4, pp. 503-514 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This paper is concerned with an inverse boundary value problem for a Boussinesq type equation of fourth order with nonlocal time integral conditions. The definition of a classical solution of the problem is introduced. The goal of this paper is to determine the unknown coefficient and to solve the problem of interest. The problem is considered in a rectangular domain. To investigate the solvability of the inverse problem, we perform a conversion from the original problem to some auxiliary inverse problem with trivial boundary conditions. By the contraction mapping principle we prove the existence and uniqueness of solutions of the auxiliary problem. Then we make a conversion to the stated problem again and, as a result, we obtain the solvability of the inverse problem.
Keywords: inverse value problem, uniqueness, classical solution.
Mots-clés : Boussinesq equation, existence 
@article{VUU_2016_26_4_a4,
     author = {Ya. T. Megraliev and F. Kh. Alizade},
     title = {Inverse boundary value problem for a {Boussinesq} type equation of fourth order with nonlocal time integral conditions of the second kind},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {503--514},
     year = {2016},
     volume = {26},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2016_26_4_a4/}
}
TY  - JOUR
AU  - Ya. T. Megraliev
AU  - F. Kh. Alizade
TI  - Inverse boundary value problem for a Boussinesq type equation of fourth order with nonlocal time integral conditions of the second kind
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2016
SP  - 503
EP  - 514
VL  - 26
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VUU_2016_26_4_a4/
LA  - ru
ID  - VUU_2016_26_4_a4
ER  - 
%0 Journal Article
%A Ya. T. Megraliev
%A F. Kh. Alizade
%T Inverse boundary value problem for a Boussinesq type equation of fourth order with nonlocal time integral conditions of the second kind
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2016
%P 503-514
%V 26
%N 4
%U http://geodesic.mathdoc.fr/item/VUU_2016_26_4_a4/
%G ru
%F VUU_2016_26_4_a4
Ya. T. Megraliev; F. Kh. Alizade. Inverse boundary value problem for a Boussinesq type equation of fourth order with nonlocal time integral conditions of the second kind. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 26 (2016) no. 4, pp. 503-514. http://geodesic.mathdoc.fr/item/VUU_2016_26_4_a4/

[1] Samarskii A. A., “On some problems of theory of differential equations”, Differ. Uravn., 16:11 (1980), 1925–1935 (in Russian)

[2] Kozhanov A. I., Pul'kina L. S., “On the solvability of boundary value problems with a nonlocal boundary condition of integral form for multidimensional hyperbolic equations”, Differential Equations, 42:9 (2006), 1233–1246 | DOI | MR | Zbl

[3] Gordeziani D. G., Avalishvili G. A., “On the constructing of solutions of the nonlocal initial boundary value problems for one-dimensional medium oscillation equations”, Matematicheskoe Modelirovanie, 12:1 (2000), 94–103 (in Russian) | Zbl

[4] Pul'kina L. S., “Boundary-value problems for a hyperbolic equation with nonlocal conditions of the I and II kind”, Russian Mathematics, 56:4 (2012), 62–69 | DOI | MR | Zbl

[5] Kirichenko S. V., “On a boundary value problem for mixed type equation with nonlocal initial conditions in the rectangle”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 2013, no. 3(32), 185–189 | DOI

[6] Varlamov V. V., “Asymptotic behavior of solutions of the damped Boussinesq equation in two space dimensions”, International Journal of Mathematics and Mathematical Sciences, 22:1 (1999), 131–145 | DOI | MR | Zbl

[7] Yan Z. Y., Xie F. D., Zhang H. Q., “Symmetry reductions, integrability and solitary wave solutions to high-order modified Boussinesq equations with damping term”, Communications in Theoretical Physics, 36:1 (2001), 1–6 | DOI | MR | Zbl

[8] Megraliev Ya. T., “Inverse boundary value problem for second order elliptic equation with additional integral condition”, Vestn. Udmurt. Univ. Mat. Mekh. Komp'yut. Nauki, 2012, no. 1, 32–40 | DOI

[9] Khudaverdiev K. I., Veliev A. A., Investigation of the one-dimensional mixed problem for a class of the pseudo-hyperbolic equations of the third order with the nonlinear operator at the right-hand side, Chashyogly, Baku, 2010, 168 pp.