Geodesic
On solvability of an inverse boundary value problem for the Boussinesq--Love equation
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 6 (2013) no. 4, pp. 485-494.

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

In the paper an inverse boundary value problem for the Boussinesq–Love equation with an integral condition of the first kind is investigated. First, the given problem is reduced to an equivalent problem in a certain sense. Then, using the Fourier method the equivalent problem is reduced to solving the system of integral equations. The existence and uniqueness of a solution to the system of integral equation is proved by the contraction mapping principle. This solution is also the unique solution to the equivalent problem. Finally, by equivalence, the theorem of existence and uniqueness of a classical solution to the given problem is proved.
Keywords: inverse boundary value problem, the Boussinesq–Love equation, Fourier method, classical solution. 
@article{JSFU_2013_6_4_a8,
     author = {Yashar T. Mehraliyev},
     title = {On solvability of an inverse boundary value problem for the {Boussinesq--Love} equation},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {485--494},
     publisher = {mathdoc},
     volume = {6},
     number = {4},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2013_6_4_a8/}
}
TY  - JOUR
AU  - Yashar T. Mehraliyev
TI  - On solvability of an inverse boundary value problem for the Boussinesq--Love equation
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2013
SP  - 485
EP  - 494
VL  - 6
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2013_6_4_a8/
LA  - en
ID  - JSFU_2013_6_4_a8
ER  - 
%0 Journal Article
%A Yashar T. Mehraliyev
%T On solvability of an inverse boundary value problem for the Boussinesq--Love equation
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2013
%P 485-494
%V 6
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2013_6_4_a8/
%G en
%F JSFU_2013_6_4_a8
Yashar T. Mehraliyev. On solvability of an inverse boundary value problem for the Boussinesq--Love equation. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 6 (2013) no. 4, pp. 485-494. http://geodesic.mathdoc.fr/item/JSFU_2013_6_4_a8/

[1] A. N. Tikhonov, “On stability of inverse problems”, Dokl. AN SSSR, 39:5 (1943), 195–198 (in Russian) | MR

[2] M. M. Lavrent'ev, “On an inverse problem for a wave equation”, Dokl. AN SSSR, 157:3 (1964), 520–521 (in Russian) | MR

[3] M. M. Lavrent'ev, V. G. Romanov, S. T. Shishatsky, Ill-posed problems of mathematical physics and analysis, Nauka, M., 1980 (in Russian) | MR

[4] V. K. Ivanov, V. V. Vasin, V. P. Tanana, Theory of linear ill-posed problems and its applications, Nauka, M., 1978 (in Russian) | MR

[5] A. M. Denisov, Introduction to theory of inverse problems, MGU, M., 1994 (in Russian)

[6] Ya. T. Mehraliyev, “Inverse boundary problem for a partial differential equation of fourth order with integral condition”, Vestnik YuUrGU. Series: “Matematika, Mehanika, Fizika”, 32(249):5 (2011), 51–56 (in Russian)

[7] Ya. T. Mehraliyev, “On one inverse boundary value problem for hyperbolic equations of second order with integral condition of the first kind”, Bryansk Gosydarstvennyi Universitet Herald, 2011, no. 4, 22–28 (in Russian)

[8] Ya. T. Mehraliyev, “On solvability of an inverse boundary value problem for a second order elliptic equation”, Vest. Tverskogo Gos. Univ., Ser. prikladnaya matematika, 2011, no. 23, 25–38 (in Russian)

[9] Ya. T. Mehraliyev, “Inverse boundary value problem for a second order elliptic equation with an additional integral condition”, Vest. Udmurtskogo Univ. Matematika. Mekhanika. Komp'yuternye Nauki, 2012, no. 1, 32–40 (in Russian)

[10] Dzh. Uizem, Linear and Nonlinear Waves, Mir, M., 1977 (in Russian)

[11] B. M. Budak, A. A. Samarskii, A. N. Tikhonov, A Collection of Problems in Mathematical Physics, Nauka, M., 1972 (in Russian) | MR