Geodesic
Inverse problem of the Boussinesq--Love equation with an extra integral condition
Sibirskij žurnal industrialʹnoj matematiki, Tome 16 (2013) no. 1, pp. 75-83

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The paper addresses an inverse boundary value problem for the Boussinesq–Love equation with an extra integral condition of the first kind. The problem is firstly reduced to the problem that is in a sense quivalent to the original. Then, the Fourier mathod is applied, reducing the problem to solution of a system of integral equations. The existence and uniqueness of the latter equation is proved by the contraction mapping principle, which also yoelds the unique solution of the equivalent problem. Using equivalence, we finally prove the unique existence of a classical solution of the problem under consideration.
Keywords: inverse boundary problem, Fourier method, classical solution.
Mots-clés : Boussinesq–Love equation 
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     author = {Ya. T. Megraliev},
     title = {Inverse problem of the {Boussinesq--Love} equation with an extra integral condition},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {75--83},
     publisher = {mathdoc},
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     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2013_16_1_a7/}
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Ya. T. Megraliev. Inverse problem of the Boussinesq--Love equation with an extra integral condition. Sibirskij žurnal industrialʹnoj matematiki, Tome 16 (2013) no. 1, pp. 75-83. http://geodesic.mathdoc.fr/item/SJIM_2013_16_1_a7/