Spectral Approach to Derive the Representation Formulae for Solutions of the Wave Equation

Gusein Sh. Guseinov

Journal of Applied Mathematics, 2012, vol. 2012, 1-19

Abstract:

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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:761248

DOI: 10.1155/2012/761248

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