Geodesic
On the boundary value problem for a three-dimensional analog of the Boussinesq differential equation
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 158 (2016) no. 3, pp. 424-433

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This paper considers the questions of solvability and construction of the solution of the nonlocal boundary value problem for a three-dimensional analog of the homogeneous fourth-order Boussinesq differential equation. The spectral method is used based on separation of variables. The criterion of solvability of the considered problem is found. The solvability of the problem is proved under this criterion.
Mots-clés : Boussinesq equation
Keywords: fourth-order equation, three-dimensional domain, integral condition, solvability. 
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     author = {T. K. Yuldashev},
     title = {On the boundary value problem for a~three-dimensional analog of the {Boussinesq} differential equation},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {424--433},
     publisher = {mathdoc},
     volume = {158},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2016_158_3_a7/}
}
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T. K. Yuldashev. On the boundary value problem for a three-dimensional analog of the Boussinesq differential equation. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 158 (2016) no. 3, pp. 424-433. http://geodesic.mathdoc.fr/item/UZKU_2016_158_3_a7/