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

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 a...

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Main Author:	Serik A. Aldashev
Format:	Article
Language:	English
Published:	Samara State Technical University 2018-07-01
Series:	Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki
Subjects:	multidimensional hyperbolic-parabolic equation Dirichlet spectral problem multidimensional cylindrical domain
Online Access:	http://mi.mathnet.ru/eng/vsgtu1585

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spelling	doaj-20510b3b29ba428996a174af0f82d3522020-11-24T22:06:43ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812018-07-0122222523510.14498/vsgtu1585A criterion for the unique solvability of the spectral Dirichlet problem for a class of multidimensional hyperbolic-parabolic equationsSerik A. Aldashev0Kazakh National Pedagogical University named after Abay, Almaty, 480100, KazakhstanIn 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. http://mi.mathnet.ru/eng/vsgtu1585multidimensional hyperbolic-parabolic equationDirichlet spectral problemmultidimensional cylindrical domain
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Serik A. Aldashev
spellingShingle	Serik A. Aldashev A criterion for the unique solvability of the spectral Dirichlet problem for a class of multidimensional hyperbolic-parabolic equations Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki multidimensional hyperbolic-parabolic equation Dirichlet spectral problem multidimensional cylindrical domain
author_facet	Serik A. Aldashev
author_sort	Serik A. Aldashev
title	A criterion for the unique solvability of the spectral Dirichlet problem for a class of multidimensional hyperbolic-parabolic equations
title_short	A criterion for the unique solvability of the spectral Dirichlet problem for a class of multidimensional hyperbolic-parabolic equations
title_full	A criterion for the unique solvability of the spectral Dirichlet problem for a class of multidimensional hyperbolic-parabolic equations
title_fullStr	A criterion for the unique solvability of the spectral Dirichlet problem for a class of multidimensional hyperbolic-parabolic equations
title_full_unstemmed	A criterion for the unique solvability of the spectral Dirichlet problem for a class of multidimensional hyperbolic-parabolic equations
title_sort	criterion for the unique solvability of the spectral dirichlet problem for a class of multidimensional hyperbolic-parabolic equations
publisher	Samara State Technical University
series	Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki
issn	1991-8615 2310-7081
publishDate	2018-07-01
description	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.
topic	multidimensional hyperbolic-parabolic equation Dirichlet spectral problem multidimensional cylindrical domain
url	http://mi.mathnet.ru/eng/vsgtu1585
work_keys_str_mv	AT serikaaldashev acriterionfortheuniquesolvabilityofthespectraldirichletproblemforaclassofmultidimensionalhyperbolicparabolicequations AT serikaaldashev criterionfortheuniquesolvabilityofthespectraldirichletproblemforaclassofmultidimensionalhyperbolicparabolicequations
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A criterion for the unique solvability of the spectral Dirichlet problem for a class of multidimensional hyperbolic-parabolic equations

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