Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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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
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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.


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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

DOI: https://doi.org/10.1090/S0033-569X-2011-01244-3
Received by editor(s): April 12, 2010
Published electronically: July 1, 2011
Article copyright: © Copyright 2011 Brown University


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