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Original Articles

A representation formula for the wave equation revisited

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Pages 371-380 | Accepted 25 Oct 2011, Published online: 23 Nov 2011
 

Abstract

We give an elementary, rigorous and self-contained derivation of a Kirchhoff representation formula for solutions of the wave equation for a bounded region in three-dimensional space for the case of non-homogeneous initial conditions. A special feature of the result is the role of spherical caps which seems not to be noticed previously. The formula is readymade for boundary integral formulations of initial/boundary-value problems for the wave operator.

AMS Subject Classifications::

Acknowledgements

We are grateful to Ivar Stakgold for advice and encouragement.

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