About solving of the first boundary-value problem for ultrahyperbolic equation in a ball (Q2901678)
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scientific article; zbMATH DE number 6062206
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | About solving of the first boundary-value problem for ultrahyperbolic equation in a ball |
scientific article; zbMATH DE number 6062206 |
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31 July 2012
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spherical functions
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Gauss hypergeometric equation
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Dirichlet problem
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About solving of the first boundary-value problem for ultrahyperbolic equation in a ball (English)
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This paper deals with the following problem NEWLINE\[NEWLINE u_{x_1x_1}+\dots +u_{x_kx_k}-a^2(u_{x_{k+1 k+1}}+\dots +u_{x_nx_n}),\,\;\text{ in\,\,} \Omega, NEWLINE\]NEWLINE NEWLINE\[NEWLINE u| | _{\partial \Omega}=0\,,NEWLINE\]NEWLINE where \(\Omega=\{ x\in R^n: \,\, | x| <1 \}\) is n-dimensional ball and \(f\) is polynomial. It is given an algorithm of construction of a formal solution of this problem, based on the use of spherical functions and Gauss hypergeometric equation.
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