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On mixed boundary value problems for the Helmholtz equation*

Published online by Cambridge University Press:  14 February 2012

R. Kress  and
G. F. Roach
R. Kress
Affiliation:
Lehrstühle für Numerische und Angewandte Mathematak, Universitat Göttingen
G. F. Roach
Affiliation:
Department of Mathematics, University of Strathclyde
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Synopsis

Existence and uniqueness theorems are obtained for a class of mixed boundary value problems associated with the three-dimensional Helmholtz equation. In this context the boundary of the region of interest is assumed to consist of the union of a finite number of disjoint, closed, bounded Lyapunov surfaces on some of which are imposed Dirichlet conditions whilst Neumann conditions are imposed on the remainder. An integral equation method is adopted throughout. The required boundary integral equations are generated by a modified layer theoretic approach which extends the work of Brakhage and Werner [1] and Leis [2, 3].

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 77 , Issue 1-2 , 1977 , pp. 65 - 77
Copyright
Copyright © Royal Society of Edinburgh 1977

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References

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3Leis, R. Vorlesungen über Partielle Differentialgleichungen zweiter Ordnung. Hochschultaschenbucher 165/165a (Mannheim: Bibliographisches Institut, 1967).Google Scholar
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