2024/12/17 by Wu, Chengyu, Yang, Jiaqing
#35R30 #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2412.12452
This paper is concerning the inverse conductive scattering of acoustic waves by a bounded inhomogeneous object with possibly embedded obstacles inside. A new uniqueness theorem is proved that the conductive object is uniquely determined by the fixed frequency far-field measurements, ignoring its contents. Meanwhile, the boundary informations of several related physical coefficients are also uniquely determined. The proof is mainly based on a detailed singularity analysis of solutions near the interface associated with a family of point sources or hypersingular point sources, which is deduced by the potential theory. Moreover, the other key ingredient in the proof is the well-posedness of the interior transmission problem with the conductivity boundary condition in the L2 sense, where several sufficient conditions depending on the domain and physical coefficients are provided.