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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Uniqueness for the determination of sound-soft defects in an inhomogeneous planar medium by acoustic boundary measurements


Author: Luca Rondi
Journal: Trans. Amer. Math. Soc. 355 (2003), 213-239
MSC (2000): Primary 35R30
DOI: https://doi.org/10.1090/S0002-9947-02-03105-7
Published electronically: September 5, 2002
MathSciNet review: 1928086
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Abstract: We consider the inverse problem of determining shape and location of sound-soft defects inside a known planar inhomogeneous and anisotropic medium through acoustic imaging at low frequency. In order to determine the defects, we perform acoustic boundary measurements, with prescribed boundary conditions of different types. We prove that at most two, suitably chosen, measurements allow us to uniquely determine multiple defects under minimal regularity assumptions on the defects and the medium containing them. Finally, we treat applications of these results to the case of inverse scattering.


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Additional Information

Luca Rondi
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Address at time of publication: Dipartimento di Scienze Matematiche, Università degli Studi di Trieste, Trieste, Italy
Email: rondi@mathsun1.univ.trieste.it

DOI: https://doi.org/10.1090/S0002-9947-02-03105-7
Received by editor(s): November 12, 2001
Received by editor(s) in revised form: March 19, 2002
Published electronically: September 5, 2002
Article copyright: © Copyright 2002 American Mathematical Society