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The three-dimensional inverse scattering problem for the Helmholtz equation

Published online by Cambridge University Press:  24 October 2008

B. D. Sleeman
B. D. Sleeman
Affiliation:
Department of Mathematics, University of Dundee, Dundee, Scotland
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Extract

In this paper we are concerned with solutions of the three-dimensional Helmholtz equation which are of class C2 (i.e. regular) in the exterior of a bounded domain D. In cylindrical polar coordinates (r, z, φ) such solutions satisfy the equation

in which we have dimensionalized the radial coordinate r so that the wave number is normalized to unity. If we further assume that u satisfies the Sommerfeld radiation condition

then u may be regarded as being generated by volume sources, surface sources, or point singularities, all of which are contained in D.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 73 , Issue 3 , May 1973 , pp. 477 - 488
Copyright
Copyright © Cambridge Philosophical Society 1973

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