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The linear sampling method for anisotropic media. (English) Zbl 1019.78003

The authors present an analysis of the linear sampling method to determine the support of an anisotropic inhomogeneous penetrable scatterer from a knowledge of the incident and scattered time harmonic acoustic wave at fixed frequency. They extend the results of D. Colton, R. Kress and P. Monk [J. Comput. Appl. Math. 81, 269-298 (1997; Zbl 0885.35143)] to the case of (possibly) complex-valued anisotropic medium that does not vary smoothly across the boundary. The method is based on an analysis of the interior transmission problem, and the paper also gives appropriate conditions under which the set of transmission eigenvalues is discrete.

MSC:

78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory
35R30 Inverse problems for PDEs
35P25 Scattering theory for PDEs

Citations:

Zbl 0885.35143
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References:

[1] Colton, D.; Coyle, J.; Monk, P., Recent developments in inverse acoustic scattering theory, SIAM Rev., 42, 3, 369-414 (2000) · Zbl 0960.76081
[2] Colton, D.; Kress, R., Inverse Acoustic and Electromagnetic Scattering Theory (1998), Springer: Springer Berlin · Zbl 0893.35138
[3] Colton, D.; Kress, R.; Monk, P., Inverse scattering from an orthotropic medium, J. Comput. Appl. Math., 81, 269-298 (1997) · Zbl 0885.35143
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[7] Coyle, J., An inverse electromagnetic scattering problem in a two-layered background, Inverse Problems, 16, 275-292 (2000) · Zbl 0973.35196
[8] Gylys-Colwell, F., An inverse problem for the Helmholtz equation, Inverse Problems, 16, 139-156 (2000) · Zbl 0860.35142
[9] Hähner, P., On the uniqueness of the shape of a penetrable, anisotropic obstacle, J. Comput. Appl. Math., 116, 167-180 (2000) · Zbl 0978.35098
[10] Hörmander, L., The Analysis of Linear differential Operators, Vol. 3 (1985), Springer: Springer Berlin
[11] Kirsch, A., Factorization of the far field operator for the inhomogeneous medium case and an application in inverse scattering theory, Inverse Problems, 15, 413-429 (1999) · Zbl 0926.35162
[12] Piana, M., On the uniqueness for anisotropic inhomogeneous inverse scattering problems, Inverse Problems, 14, 1565-1579 (1998) · Zbl 0920.35170
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