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

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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},
     publisher = {mathdoc},
     volume = {26},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2016_26_4_a4/}
}
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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/