The direct scattering problem: Uniqueness and existence for anisotropic media
Author:
Panagiotis Emmanouil
Journal:
Quart. Appl. Math. 69 (2011), 747-758
MSC (2000):
Primary 35P25, 47A40, 45A05, 45B05
DOI:
https://doi.org/10.1090/S0033-569X-2011-01244-3
Published electronically:
July 1, 2011
MathSciNet review:
2893998
Full-text PDF Free Access
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Abstract: In this paper, we investigate the problem of the transmission of plane acoustic waves through a penetrable inhomogeneous body with an impenetrable core. Firstly, we discretize the inhomogeneous body via means of a multi-layer, multi- subdivision approach. Then, we prove the uniqueness and existence of solutions to this problem. Finally, we conclude with a discussion of potential applications and what remains to be done.
References
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References
- A. KIRSCH: The MUSIC algorithm and the factorization method in inverse scattering theory for inhomogeneous media, Inverse Problems, 18 (4) (2002), 1025–1040. MR 1929280 (2003f:35286)
- G. DASSIOS and R. KLEINMAN: Low frequency scattering, Oxford Univ. Press, Oxford, 2000. MR 1858914 (2003a:35001)
- F. CAKONI and D. COLTON: Qualitative methods in inverse scattering theory, Springer, Berlin, 2006. MR 2256477 (2008c:35334)
- C. ATHANASIADIS: The multi-layered ellipsoid with a soft core in the presence of a low-frequency acoustic wave, Q. J. Mech. Appl. Math., 47 (1994), 441-459.
- C. ATHANASIADIS and I.G. STRATIS: Low-frequency acoustic scattering by an infinitely stratified scatterer, Rend. Mat. Appl. 15 (1995), 133-152. MR 1330184 (96d:35142)
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Additional Information
Panagiotis Emmanouil
Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark, Delaware, 19716, USA
Email:
emmanouil.panagiotis@gmail.com
Received by editor(s):
April 12, 2010
Published electronically:
July 1, 2011
Article copyright:
© Copyright 2011
Brown University