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8.—Constructive Methods for Solving the Exterior Neumann Problem for the Reduced Wave Equation in a Spherically Symmetric Medium*

Published online by Cambridge University Press:  14 February 2012

David Colton  and
Wolfgang Wendland
David Colton
Affiliation:
Department of Mathematics, University of Strathclyde
Wolfgang Wendland
Affiliation:
Fachbereich Mathematik, Technische Hochschule, Darmstadt.
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Synopsis

An integral operator is constructed which maps solutions of the reduced wave equation defined in exterior domains onto solutions of ∆n u+λ2(l+B(r))u = 0 (*) defined in exterior domains, where B(r) is a continuously differentiable function of compact support. This operator is then used to construct a solution to the exterior Neumann problem for (*) satisfying the Sommerfeld radiation condition at infinity. Such problems arise in connection with the scattering of acoustic waves in a non-homogeneous medium, and this paper gives a method for solving these problems which is suitable for analytic and numerical approximations.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 75 , Issue 2 , 1976 , pp. 97 - 107
Copyright
Copyright © Royal Society of Edinburgh 1976

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References

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