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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2014, Issue 3(36), Pages 21–30
DOI: https://doi.org/10.14498/vsgtu1300 (Mi vsgtu1300) 		 
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

S. A. Aldashev

Kazakh National Pedagogical University, Almaty, 480100, Kazakhstan
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DOI: https://doi.org/10.14498/vsgtu1300
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.
Keywords: multidimensional hyperbolic equation, Dirichlet spectral problem, multidimensional cylindrical domain, solvability, uniqueness.
Original article submitted 04/III/2014
revision submitted – 26/V/2014
Bibliographic databases:
Document Type: Article
UDC: 517.956.328
MSC: 35L05, 35R25, 35A01, 35A02
Language: Russian
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
Citation in format AMSBIB
\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
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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