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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, 2018, Volume 22, Number 2, Pages 225–235
DOI: https://doi.org/10.14498/vsgtu1585 (Mi vsgtu1585) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Differential Equations and Mathematical Physics

A criterion for the unique solvability of the spectral Dirichlet problem for a class of multidimensional hyperbolic-parabolic equations

S. A. Aldashev

Kazakh National Pedagogical University named after Abay, Almaty, 480100, Kazakhstan
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DOI: https://doi.org/10.14498/vsgtu1585
Abstract: In the cylindrical domain of Euclidean space for one class of multidimensional hyperbolic parabolic equations the spectral Dirichlet problem with homogeneous boundary conditions is considered. The solution is sought in the form of an expansion in multidimensional spherical functions. The existence and uniqueness theorems of the solution are proved. Conditions for the unique solvability of the problem are obtained, which essentially depend on the height of the cylinder.
Keywords: multidimensional hyperbolic-parabolic equation, Dirichlet spectral problem, multidimensional cylindrical domain.
Received: December 5, 2017
Revised: April 8, 2018
Accepted: June 11, 2018
First online: July 1, 2018
Bibliographic databases:
Document Type: Article
UDC: 517.955.2:517.956
MSC: 35M12, 35A02
Language: Russian
Citation: S. A. Aldashev, “A criterion for the unique solvability of the spectral Dirichlet problem for a class of multidimensional hyperbolic-parabolic equations”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 22:2 (2018), 225–235
Citation in format AMSBIB
\Bibitem{Ald18}
\by S.~A.~Aldashev
\paper A criterion for the unique solvability of the spectral Dirichlet problem for a class of multidimensional hyperbolic-parabolic equations
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2018
\vol 22
\issue 2
\pages 225--235
\mathnet{http://mi.mathnet.ru/vsgtu1585}
\crossref{https://doi.org/10.14498/vsgtu1585}
\zmath{https://zbmath.org/?q=an:07038283}
\elib{https://elibrary.ru/item.asp?id=35467728}
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    • This publication is cited in the following 1 articles:
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