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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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