Abstract
We consider the interior inverse scattering problem for recovering the shape of a penetrable partially coated cavity with external obstacles from the knowledge of measured scattered waves due to point sources. In the first part, we obtain the well-posedness of the direct scattering problem by the variational method. In the second part, we establish the mathematical basis of the linear sampling method to recover both the shape of the cavity, and the shape of the external obstacle, however the exterior transmission eigenvalue problem also plays a key role in the discussion of this paper.
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The first author was supported by the Natural Science Foundation of Xinjiang Uygur Autonomous Region of China (2019D01A05); The second author was supported by the NSFC (11571132).
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Ye, J., Yan, G. The Linear Sampling Method for Reconstructing a Penetrable Cavity with Unknown External Obstacles. Acta Math Sci 43, 751–776 (2023). https://doi.org/10.1007/s10473-023-0216-2
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DOI: https://doi.org/10.1007/s10473-023-0216-2
Key words
- inverse scattering
- mixed boundary value problem
- exterior transmission eigenvalue
- interior measurements
- linear sampling method