Geodesic
A criterion for the unique solvability of the Dirichlet spectral problem in a cylindrical domain for multidimensional hyperbolic equations with wave operator
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 3 (2014), pp. 21-30

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We consider the Dirichlet spectral problem with the homogeneous boundary conditions in a cylindrical domain of Euclidean space for multidimensional hyperbolic equation with wave operator. We construct the solution as an expansion in multidimensional spherical functions; prove the existence and uniqueness theorems. The obtained conditions of the problem unique solvability essentially depend on the “height” of the cylinder.
Keywords: multidimensional hyperbolic equation, Dirichlet spectral problem, multidimensional cylindrical domain, solvability, uniqueness. 
@article{VSGTU_2014_3_a1,
     author = {S. A. Aldashev},
     title = {A criterion for the unique solvability of the {Dirichlet} spectral problem in a cylindrical domain for multidimensional hyperbolic equations with wave operator},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {21--30},
     publisher = {mathdoc},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2014_3_a1/}
}
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S. A. Aldashev. A criterion for the unique solvability of the Dirichlet spectral problem in a cylindrical domain for multidimensional hyperbolic equations with wave operator. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 3 (2014), pp. 21-30. http://geodesic.mathdoc.fr/item/VSGTU_2014_3_a1/