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

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...

Full description

Bibliographic Details
Main Author: Gusein Sh. Guseinov
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2012/761248
id doaj-4156d9820a74412ab6fa6a7b20ad6fca
record_format Article
spelling doaj-4156d9820a74412ab6fa6a7b20ad6fca2020-11-24T22:49:54ZengHindawi LimitedJournal 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
collection DOAJ
language English
format Article
sources DOAJ
author Gusein Sh. Guseinov
spellingShingle Gusein Sh. Guseinov
Spectral Approach to Derive the Representation Formulae for Solutions of the Wave Equation
Journal of Applied Mathematics
author_facet Gusein Sh. Guseinov
author_sort Gusein Sh. Guseinov
title 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_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_sort spectral approach to derive the representation formulae for solutions of the wave equation
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2012-01-01
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.
url http://dx.doi.org/10.1155/2012/761248
work_keys_str_mv AT guseinshguseinov spectralapproachtoderivetherepresentationformulaeforsolutionsofthewaveequation
_version_ 1725674405876465664

Similar Items