On Uniqueness in the General Inverse Transmisson Problem |
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Authors: | Victor Isakov |
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Institution: | (1) Department of Mathematics and Statistics, Wichita State University, Wichita, KS 67206, USA |
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Abstract: | In this paper we demonstrate uniqueness of a transparent obstacle, of coefficients of rather general boundary transmission
condition, and of a potential coefficient inside obstacle from partial Dirichlet-to Neumann map or from complete scattering
data at fixed frequency. The proposed transmission problem includes in particular the isotropic elliptic equation with discontinuous
conductivity coefficient. Uniqueness results are shown to be optimal. Hence the considered form can be viewed as a canonical
form of isotropic elliptic transmission problems. Proofs use singular solutions of elliptic equations and complex geometrical
optics. Determining an obstacle and boundary conditions (i.e. reflecting and transmitting properties of its boundary and interior)
is of interest for acoustical and electromagnetic inverse scattering, for modeling fluid/structure interaction, and for defects
detection. |
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Keywords: | |
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