GENERALIZED RELLICH'S LEMMAS, UNIQUENESS THEOREM AND INSIDE-OUTSIDE DUALITY FOR SCATTERING POLES
Document Type
Article
Publication Date
1-1-2026
Abstract
Scattering poles correspond to non-trivial scattered fields in the absence of incident waves and play a crucial role in the study of wave phenomena. These poles are complex wavenumbers with negative imaginary parts. In this paper, we prove two generalized Rellich’s lemmas for scattered fields associated with complex wavenumbers. These lemmas are then used to establish uniqueness results for inverse scattering problems. We further explore the inside-outside duality, which characterizes scattering poles through the linear sampling method applied to interior scattering problems. Notably, we demonstrate that exterior Dirichlet/Neumann poles can be identified without prior knowledge of the actual sound-soft or sound-hard obstacles. Numerical examples are provided to validate the theoretical results.
Publication Title
Inverse Problems and Imaging
Recommended Citation
Liu, X.,
Sun, J.,
&
Zhang, L.
(2026).
GENERALIZED RELLICH'S LEMMAS, UNIQUENESS THEOREM AND INSIDE-OUTSIDE DUALITY FOR SCATTERING POLES.
Inverse Problems and Imaging,
24, 34-52.
http://doi.org/10.3934/ipi.2026004
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p2/2540