×

zbMATH — the first resource for mathematics

On recovering obstacles inside inhomogeneities. (English) Zbl 0915.35116
Authors’ abstract: “We consider acoustic scattering from an obstacle inside an inhomogeneous structure. We prove that if the outside inhomogeneity is known then the obstacle and possible inside inhomogeneity are uniquely determined by the fixed energy far field data. The proof is based on new mapping properties of layer potentials in spaces that specify one point”.

MSC:
35R30 Inverse problems for PDEs
35P25 Scattering theory for PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] and , Integral Equation Methods in Scattering Theory, Wiley, New York, 1983.
[2] and , Inverse Acoustic and Electromagnetic Scattering Theory, Springer, Berlin, 1992. · Zbl 0760.35053
[3] Gerlach, Inverse Problems 12 pp 619– (1996)
[4] and , Elliptic Partial Differential Equations of Second Order, Springer, Berlin, 1977.
[5] Hähner, J. Diff. Equations 128 pp 300– (1996)
[6] Isakov, Commun. Part. Diff. Eq. 15 pp 1565– (1990)
[7] Kirsch, Inverse Problems 9 pp 285– (1993)
[8] Nachman, Annals of Math. 128 pp 531– (1988)
[9] Novikov, Translation in Func. Anal. and its Appl. 22 pp 263– (1988)
[10] Ramm, Inverse Problems 4 pp 877– (1988) · Zbl 0713.35096
[11] Sylvester, Annals. of Math. 125 pp 153– (1987)
[12] Reconstruction of an obstacle inside a planar domain from boundary measurements, Manuscript, 1995.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.