Non-homogeneous wave equation on a cone

Non-homogeneous wave equation on a cone

The wave equation in the cone is shown to have a unique solution if u and its partial derivatives in x are in on the cone, and the solution can be explicit given in the Fourier series of orthogonal polynomials on the cone. This provides a particular solution for the boundary value problems of the no...

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Bibliographic Details
Published in:Integral transforms and special functions Vol. 32; no. 5-8; pp. 604 - 619
Main Authors: Olver, Sheehan, Xu, Yuan
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 03-08-2021
Taylor & Francis Ltd
Subjects:
Boundary value problems
cone
Fourier series
orthogonal polynomials
orthogonal series
Polynomials
Wave equation
Wave equations
Online Access:Get full text
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Summary:The wave equation in the cone is shown to have a unique solution if u and its partial derivatives in x are in on the cone, and the solution can be explicit given in the Fourier series of orthogonal polynomials on the cone. This provides a particular solution for the boundary value problems of the non-homogeneous wave equation on the cone, which can be combined with a solution to the homogeneous wave equation in the cone to obtain the full solution.
ISSN:1065-2469
1476-8291
DOI:10.1080/10652469.2020.1808633