Geodesic
An inverse problem for a fourth-order Boussinesq equation with non-conjugate boundary and integral overdetermination conditions
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2017), pp. 17-36

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The work is devoted to the study of the solvability of the inverse boundary value problem with an unknown time depended coefficient for a fourth-order Boussinesq equation with non-conjugate boundary conditions and integral overdetermination conditions. The goal of paper consists of determination of the unknown coefficient and the solution of the considered problem. 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 direct auxiliary problem with trivial boundary conditions. Further, we prove the solvability of the supplementary inverse problem. Then we make a conversion to the stated problem again and as a result we receive the solvability of the inverse problem.
Keywords: inverse boundary problem, Fourier method, classical solution.
Mots-clés : Boussinesq equation 
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     author = {Ya. T. Megraliev and F. H. Alizade},
     title = {An inverse problem for a fourth-order {Boussinesq} equation with non-conjugate boundary and integral overdetermination conditions},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {17--36},
     publisher = {mathdoc},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2017_2_a1/}
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Ya. T. Megraliev; F. H. Alizade. An inverse problem for a fourth-order Boussinesq equation with non-conjugate boundary and integral overdetermination conditions. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2017), pp. 17-36. http://geodesic.mathdoc.fr/item/VTPMK_2017_2_a1/