Abstract
We establish the uniqueness of the solution of the inverse problem for the Helmholtz equation in which the refraction coefficient, which describes the properties of a bounded inhomogeneity in a wave medium, is sought. The initial data for determining the desired coefficient are the absolute values of the solutions corresponding to either point sources concentrated on a segment or spherically symmetric distributed sources with centers on the segment. The measurements of the wave field are carried out in a plane domain that does not meet the inhomogeneity localization area.
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This work was supported by the Russian Science Foundation, project no. 20-11-20085.
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Translated by V. Potapchouck
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Kokurin, M.Y. On the Uniqueness of the Solution of the Inverse Coefficient Problem for the Helmholtz Equation in a Phaseless Spatially Nonoverdetermined Statement. Diff Equat 57, 1136–1141 (2021). https://doi.org/10.1134/S0012266121090020
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DOI: https://doi.org/10.1134/S0012266121090020