Uniqueness for the determination of sound-soft defects in an inhomogeneous planar medium by acoustic boundary measurements
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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.References
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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
- Received by editor(s): November 12, 2001
- Received by editor(s) in revised form: March 19, 2002
- Published electronically: September 5, 2002
- © Copyright 2002 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 355 (2003), 213-239
- MSC (2000): Primary 35R30
- DOI: https://doi.org/10.1090/S0002-9947-02-03105-7
- MathSciNet review: 1928086