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A transmission problem for the plate equation

Published online by Cambridge University Press:  14 November 2011

R. Leis  and
G. F. Roach
R. Leis
Affiliation:
Institut für Angewandte Mathematik, Universität Bonn, B.R.D.
G. F. Roach
Affiliation:
Department of Mathematics, University of Strathclyde, Glasgow
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Synopsis

A scattering theory is developed for transmission problems associated with the plate equation. Asymptotic methods of solution for large time are examined as are questions concerning regularity of solution, nature of the associated spectrum and existence of appropriate wave operators. It is shown that in contrast to solutions of the wave equation, signals can propagate with an infinite dispersion velocity.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 99 , Issue 3-4 , 1985 , pp. 285 - 312
Copyright
Copyright © Royal Society of Edinburgh 1985

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References

1Belopoloskii, A. L. and Birman, M. S.. The existence of wave operators in the theory of scattering with a pair of spaces. Math. USSR-lzv. 2 (1968), 1117–1130.CrossRefGoogle Scholar
2Bröhl, A.. Zur Streutheorie für die Plattengleichung. Bonner Math. Schriften Nr 122 (1980).Google Scholar
3Leis, R.. Auβenraumaufgaben zur Plattengleichung. Arch. Rational Mech. Anal. 35 (1969), 226–233.CrossRefGoogle Scholar
4Leis, R.. Zur Theorie der Plattengleichung. Bonn, Bericht 101, St. Augustin 1975.Google Scholar
5Leis, R.. Anfangsrandwertaufgaben der mathematischen Physik. Vorlesungsreihe, Sonderforschungsbereich 72, Nr 9 (Bonn, 1982).Google Scholar
6Littman, W.. Fourier transforms of surface carried measures and the differentiability of surface averages. Bull. Amer. Math. Soc. 69 (1963), 766–770.CrossRefGoogle Scholar
7Matsumura, M.. Comportement des solutions de quelques problemes mixtes pour certain systèmes hyperboliques symmetriques a coefficients constants. Publ. Res. Inst. Math. Sci. 4 (1968), 309–359.CrossRefGoogle Scholar
8Matsumura, M.. Uniform estimates of elementary solutions of first order systems of partial differential equations. Publ. Res. Inst. Math. Sci. 6 (1970), 293–305.CrossRefGoogle Scholar
9Ortner, N.. Regularisierte Faltung von Distributionen. Z. Angew. Math. Phys. 31 (1980), 133–173.CrossRefGoogle Scholar
10Pearson, D.. A Generalisation of the Birman trace theorem. J Fund. Anal. 28 (1978), 182–186.CrossRefGoogle Scholar
11Picard, R. and Seidler, S.. A remark on two Hilbert space scattering theory. Sonderforschungsbereich 72, No. 656 (Bonn, 1984).Google Scholar
12Wilcox, C.. Scattering theory for the d'Alembert equation in exterior domains. Lecture Notes in Mathematics 442 (Berlin: Springer, 1975).Google Scholar