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Spectral representation and scattering theory for the wave equation with two unbounded media

Published online by Cambridge University Press:  24 October 2008

G. F. Roach  and
Bo Zhang
G. F. Roach
Affiliation:
Department of Mathematics, University of Strathclyde, Glasgow G1 1XH, Scotland
Bo Zhang
Affiliation:
Department of Mathematics, University of Strathclyde, Glasgow G1 1XH, Scotland
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Abstract

In this paper, we establish the generalized eigenfunction expansions for wave propagation in inhomogeneous, penetrable media in ℝn(n ≥ 2) with an unbounded interface. We then use them together with the method of stationary phase to prove the existence of the wave operators and to obtain the representations of the wave operators in terms of the generalized Fourier transforms.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 113 , Issue 2 , March 1993 , pp. 423 - 447
Copyright
Copyright © Cambridge Philosophical Society 1993

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