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Transmission problems for the vector Helmholtz equation

Published online by Cambridge University Press:  14 November 2011

Peter Wilde
Peter Wilde
Affiliation:
Institut für Numerische und Angewandte Mathematik, Lotzestraße 16-18, D-3400 Göttingen, Federal Republic of Germany
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Synopsis

Transmission problems for the vector Helmholtz equation are considered. By using boundary integral equation methods, existence and uniqueness theorems in the form of Fredholm's alternative are established.

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Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 105 , Issue 1 , 1987 , pp. 61 - 76
Copyright
Copyright © Royal Society of Edinburgh 1987

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References

1Colton, D. and Kress, R.. Integral equation methods in scattering theory (New York: Wiley-Interscience, 1983).Google Scholar
2Jörgens, K.. Lineare Integraloperatoren (Stuttgart: Teubner-Verlag, 1970).CrossRefGoogle Scholar
3Kittappa, R.. Transition problems for the Helmholtz equation. AFOSR Scientific Report, Grand 69-1794, University of Delaware, 1973.Google Scholar
4Kittappa, R. and Kleinman, R. E.. Acoustic scattering by penetrable homogeneous objects. J. Math. Phys. 16 (1975), 421–432.CrossRefGoogle Scholar
5Kleinman, R. E. and Roach, G.. On the unique solvability of a class of modified boundary integral equations. Proc. Edinburgh Math. Soc. 27 (1984), 303–311.CrossRefGoogle Scholar
6Kleinman, R. E. and Roach, G.. New integral equations for scattering by penetrable objects, II. Radio Science 19(5) (1984), 1185–1193.CrossRefGoogle Scholar
7Knauff, W. and Kress, R.. On the exterior boundary-value problem for the time-harmonic Maxwell equations. J. Math. Anal. Appl. 72 (1979), 215–235.CrossRefGoogle Scholar
8Kress, R.. On the Fredholm Alternative. Integral Equations Operator Theory 6 (1983), 453–457.CrossRefGoogle Scholar
9Kress, R.. On the boundary operator in electromagnetic scattering. Proc. Roy. Soc. Edinburgh Sect. A 103 (1986), 91–98.CrossRefGoogle Scholar
10Kress, R. and Roach, G. F.. Transmission problems for the Helmholtz equation. J.Math. Phys. 19 (1978), 1433–1437.CrossRefGoogle Scholar
11Kupradze, W. D., Randwertaufgaben der Schwingungstheorie und Integralgleichungen (Berlin: Deutscher Verlag der Wissenschaften, 1956).Google Scholar
12Martensen, E.. Potentialtheorie (Stuttgart: Teubner-Verlag, 1968).Google Scholar
13Möller, C.. Grundprobleme der mathematischen Theorie elektromagnetischer Schwingungen (Berlin: Springer, 1957).CrossRefGoogle Scholar
14Ramm, A. G.. Scattering by a penetrable body. J. Math. Phys. 25 (1984), 469–471.CrossRefGoogle Scholar
15Rellich, F.. Über das asymptotische Verhalten der Lösungen von Δu+ λu = 0 in unendlichen Gebieten. Jahresber. Deutsch. Math.-Verein. 53 (1943), 57–65.Google Scholar
16Wendland, W.. Die Fredholmsche Alternative fÜr Operatoren, die bezüglich eines bilinearen Funktionals adjungiert sind. Math. Z. 101 (1967), 61–64.CrossRefGoogle Scholar
17Wendland, W.. Bemerkungen uber die Fredholmschen Sätze. Meth. Verf. Math. Phys. 3 (1970), 141–176.Google Scholar
18Werner, P.. Zur mathematischen Theorie akustischer Wellenfelder. Arch. Rational Mech. Anal. 6 (1960), 231–260.CrossRefGoogle Scholar
19Werner, P.. Randwertprobleme der mathematischen Akustik. Arch. Rational Mech. Anal. 10 (1962), 29–66.CrossRefGoogle Scholar
20Werner, P.. Beugungsprobleme der mathematischen Akustik. Arch. Rational Mech. Anal. 12 (1963), 155–184.CrossRefGoogle Scholar
21Wilde, P.. Über Transmissionsprobleme bei der vektoriellen Helmholtzgleichung. Dissertation, Universitat Gottingen, 1985.Google Scholar