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Transmission problems for the vector Helmholtz equation

  • Peter Wilde (a1)
Synopsis
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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1Colton D. and Kress R.. Integral equation methods in scattering theory (New York: Wiley-Interscience, 1983).
2Jörgens K.. Lineare Integraloperatoren (Stuttgart: Teubner-Verlag, 1970).
3Kittappa R.. Transition problems for the Helmholtz equation. AFOSR Scientific Report, Grand 69-1794, University of Delaware, 1973.
4Kittappa R. and Kleinman R. E.. Acoustic scattering by penetrable homogeneous objects. J. Math. Phys. 16 (1975), 421432.
5Kleinman R. E. and Roach G.. On the unique solvability of a class of modified boundary integral equations. Proc. Edinburgh Math. Soc. 27 (1984), 303311.
6Kleinman R. E. and Roach G.. New integral equations for scattering by penetrable objects, II. Radio Science 19(5) (1984), 11851193.
7Knauff W. and Kress R.. On the exterior boundary-value problem for the time-harmonic Maxwell equations. J. Math. Anal. Appl. 72 (1979), 215235.
8Kress R.. On the Fredholm Alternative. Integral Equations Operator Theory 6 (1983), 453457.
9Kress R.. On the boundary operator in electromagnetic scattering. Proc. Roy. Soc. Edinburgh Sect. A 103 (1986), 9198.
10Kress R. and Roach G. F.. Transmission problems for the Helmholtz equation. J.Math. Phys. 19 (1978), 14331437.
11Kupradze W. D., Randwertaufgaben der Schwingungstheorie und Integralgleichungen (Berlin: Deutscher Verlag der Wissenschaften, 1956).
12Martensen E.. Potentialtheorie (Stuttgart: Teubner-Verlag, 1968).
13Möller C.. Grundprobleme der mathematischen Theorie elektromagnetischer Schwingungen (Berlin: Springer, 1957).
14Ramm A. G.. Scattering by a penetrable body. J. Math. Phys. 25 (1984), 469471.
15Rellich F.. Über das asymptotische Verhalten der Lösungen von Δu+ λu = 0 in unendlichen Gebieten. Jahresber. Deutsch. Math.-Verein. 53 (1943), 5765.
16Wendland W.. Die Fredholmsche Alternative fÜr Operatoren, die bezüglich eines bilinearen Funktionals adjungiert sind. Math. Z. 101 (1967), 6164.
17Wendland W.. Bemerkungen uber die Fredholmschen Sätze. Meth. Verf. Math. Phys. 3 (1970), 141176.
18Werner P.. Zur mathematischen Theorie akustischer Wellenfelder. Arch. Rational Mech. Anal. 6 (1960), 231260.
19Werner P.. Randwertprobleme der mathematischen Akustik. Arch. Rational Mech. Anal. 10 (1962), 2966.
20Werner P.. Beugungsprobleme der mathematischen Akustik. Arch. Rational Mech. Anal. 12 (1963), 155184.
21Wilde P.. Über Transmissionsprobleme bei der vektoriellen Helmholtzgleichung. Dissertation, Universitat Gottingen, 1985.
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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
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