This article is cited in 1 scientific paper (total in 1 paper)
Differential Equations
A criterion for the unique solvability of the Dirichlet spectral problem in a cylindrical domain for multidimensional hyperbolic equations with wave operator
Abstract:
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.
Citation:
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”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 3(36) (2014), 21–30
\Bibitem{Ald14}
\by S.~A.~Aldashev
\paper A criterion for the unique solvability of the Dirichlet spectral problem in a cylindrical domain for multidimensional hyperbolic equations with wave operator
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2014
\vol 3(36)
\pages 21--30
\mathnet{http://mi.mathnet.ru/vsgtu1300}
\crossref{https://doi.org/10.14498/vsgtu1300}
\zmath{https://zbmath.org/?q=an:06968914}
\elib{https://elibrary.ru/item.asp?id=23085708}
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https://www.mathnet.ru/eng/vsgtu/v136/p21
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