Spectral Approach to Derive the Representation Formulae for Solutions of the Wave Equation
Using spectral properties of the Laplace operator and some structural formula for rapidly decreasing functions of the Laplace operator, we offer a novel method to derive explicit formulae for solutions to the Cauchy problem for classical wave equation in arbitrary dimensions. Among them are the well...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/761248 |
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| _version_ | 1832549927273627648 |
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| author | Gusein Sh. Guseinov |
| author_facet | Gusein Sh. Guseinov |
| author_sort | Gusein Sh. Guseinov |
| collection | DOAJ |
| description | Using spectral properties of the Laplace operator and some structural formula for rapidly decreasing functions of the Laplace operator, we offer a novel method to derive explicit formulae for solutions to the Cauchy problem for classical wave equation in arbitrary dimensions. Among them are the well-known d'Alembert, Poisson, and Kirchhoff representation formulae in low space dimensions. |
| format | Article |
| id | doaj-art-4156d9820a74412ab6fa6a7b20ad6fca |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-4156d9820a74412ab6fa6a7b20ad6fca2025-02-03T06:08:16ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/761248761248Spectral Approach to Derive the Representation Formulae for Solutions of the Wave EquationGusein Sh. Guseinov0Department of Mathematics, Atilim University, Incek, 06836 Ankara, TurkeyUsing spectral properties of the Laplace operator and some structural formula for rapidly decreasing functions of the Laplace operator, we offer a novel method to derive explicit formulae for solutions to the Cauchy problem for classical wave equation in arbitrary dimensions. Among them are the well-known d'Alembert, Poisson, and Kirchhoff representation formulae in low space dimensions.http://dx.doi.org/10.1155/2012/761248 |
| spellingShingle | Gusein Sh. Guseinov Spectral Approach to Derive the Representation Formulae for Solutions of the Wave Equation Journal of Applied Mathematics |
| title | Spectral Approach to Derive the Representation Formulae for Solutions of the Wave Equation |
| title_full | Spectral Approach to Derive the Representation Formulae for Solutions of the Wave Equation |
| title_fullStr | Spectral Approach to Derive the Representation Formulae for Solutions of the Wave Equation |
| title_full_unstemmed | Spectral Approach to Derive the Representation Formulae for Solutions of the Wave Equation |
| title_short | Spectral Approach to Derive the Representation Formulae for Solutions of the Wave Equation |
| title_sort | spectral approach to derive the representation formulae for solutions of the wave equation |
| url | http://dx.doi.org/10.1155/2012/761248 |
| work_keys_str_mv | AT guseinshguseinov spectralapproachtoderivetherepresentationformulaeforsolutionsofthewaveequation |