Geodesic
An inverse boundary value problem for a single fourth-order Boussinesq equation with an integral condition
Čebyševskij sbornik, Tome 14 (2013) no. 4, pp. 167-179.

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In this paper an inverse boundary problem for the fourth order Boussinesq equation with integral conditions is investigated. First of all the initial problem reduced to the equivalent problem, for which the theorem of existence and uniqueness proved. Then using these facts the existence and uniqueness of the classical solution of initial problem is proved.
Keywords: Inverse boundary problem, Boussinesq equation, method Fourier, classic solution. 
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Y. T. Megraliev; F. Kh. Alizade. An inverse boundary value problem for a single fourth-order Boussinesq equation with an integral condition. Čebyševskij sbornik, Tome 14 (2013) no. 4, pp. 167-179. http://geodesic.mathdoc.fr/item/CHEB_2013_14_4_a14/

[1] Boussinesq J., “Theorie des ondes et des remous qui se propagent le long d'un canal rectangulaire horizontal, en communiquant au liquide content dans ce canal des vitesses sensiblement pareilles de surface au fond”, J. Math. Pures Appl., 17 (1872), 55–108

[2] Clarkson P., “A New exact solutions of the Boussinesq equation”, European J. Appl. Math., 1 (1990), 279–300 | DOI | MR | Zbl

[3] Hirota R., “Classical Boussinesq equation is a reduction of the modified KP equation”, J. Phys. Soc. Japan, 54 (1985), 2409–2415 | DOI | MR

[4] Z. Y. Yan, F. D. Xie, H. Q. Zhang, “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 | MR | Zbl

[5] Varlamov V. V., “Asimtotika pri bolshikh vremenakh resheniya uravneniya Bussineska s dissipatsiei”, Zhurn. vychisl. mat. i mat. fizika, 34:8–9 (1994), 1194–1205 | MR | Zbl

[6] Megraliev Ya. T., “Obratnaya kraevaya zadacha dlya differentsialnogo uravneniya s chastnymi proizvodnymi chetvertogo poryadka s integralnym usloviem”, Vestnik YuUrGU. Ser. Matematika. Mekhanika. Fizika, 2011, no. 32(249), vyp. 5, 51–56

[7] Megraliev Ya. T., “Ob odnoi obratnoi kraevoi zadache dlya giperbolicheskogo uravneniya vtorogo poryadka s integralnym usloviem pervogo roda”, Vestnik Bryanskogo gosudarstvennogo universiteta, 2011, no. 4, 22–28

[8] Budak B. M., Samarskii A. A., Tikhonov A. N., Sbornik zadach po matematicheskoi fizike, Nauka, M., 1972 | MR | Zbl

[9] Khudaverdiev K. I., Veliev A. A., Issledovanie odnomernoi smeshannoi zadachi dlya odnogo klassa psevdogiperbolicheskikh uravnenii tretego poryadka s nelineinoi operatornoi pravoi chastyu, Chashyogly, Baku, 2010