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Radiation condition and limiting amplitude principle for acoustic propagators with two unbounded media

Published online by Cambridge University Press:  14 November 2011

Bo Zhang
Bo Zhang
Affiliation:
Department of Mathematics and Statistics, Brunel University, Uxbridge UB8 3PH, U.K.
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Extract

Consider the diffraction problem for perturbed acoustic propagators with perturbations decreasing slowly at infinity. The propagation speed is discontinuous at the interface of two unbounded media, and the interface may be an arbitrary and smooth surface locally. A Sommerfeld radiation condition is introduced for the acoustic propagator, and is then used to establish the limiting absorption principle and the resolvent estimate at low frequencies for such an operator. Furthermore, we prove the existence of a unique solution to the diffraction problem and the validity of the limiting amplitude principles for the acoustic propagator.

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Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 1 , 1998 , pp. 173 - 192
Copyright
Copyright © Royal Society of Edinburgh 1998

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