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Determining a sound-soft polyhedral scatterer by a single far-field measurement
Author(s):
Giovanni
Alessandrini;
Luca
Rondi
Journal:
Proc. Amer. Math. Soc.
133
(2005),
1685-1691.
MSC (2000):
Primary 35R30;
Secondary 35P25
Posted:
January 13, 2005
MathSciNet review:
2120253
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Abstract:
We prove that a sound-soft polyhedral scatterer is uniquely determined by the far-field pattern corresponding to an incident plane wave at one given wavenumber and one given incident direction.
References:
-
- 1.
- J. Cheng and M. Yamamoto, Uniqueness in an inverse scattering problem within non-trapping polygonal obstacles with at most two incoming waves, Inverse Problems 19 (2003), pp. 1361-1384. MR 2036535 (2004k:35394)
- 2.
- D. Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, Springer-Verlag, Berlin Heidelberg New York, 1998. MR 1635980 (99c:35181)
- 3.
- H. S. M. Coxeter, Regular Polytopes, Dover, New York, 1973. MR 0370327 (51:6554)
- 4.
- C. Liu and A. Nachman, A scattering theory analogue of a theorem of Polya and an inverse obstacle problem, preprint (1994).
- 5.
- A. G. Ramm and A. Ruiz, Existence and uniqueness of scattering solutions in non-smooth domains, J. Math. Anal. Appl. 201 (1996), pp. 329-338. MR 1396903 (97b:35039)
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Additional Information:
Giovanni
Alessandrini
Affiliation:
Dipartimento di Matematica e Informatica, Università degli Studi di Trieste, Trieste, Italy
Email:
alessang@univ.trieste.it
Luca
Rondi
Affiliation:
Dipartimento di Matematica e Informatica, Università degli Studi di Trieste, Trieste, Italy
Email:
rondi@univ.trieste.it
DOI:
10.1090/S0002-9939-05-07810-X
PII:
S 0002-9939(05)07810-X
Keywords:
Inverse acoustic scattering,
polyhedra,
uniqueness,
reflection principle
Received by editor(s):
January 22, 2004
Posted:
January 13, 2005
Additional Notes:
This work was supported in part by MIUR under grant no.~2002013279.
Communicated by:
M. Gregory Forest
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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