Geometrical Characterizations of Non-Radiating Sources at Polyhedral and Conical Corners with Applications (Communications in Mathematical Research, 2023)
Considering the acoustic source scattering problems, when the source is non-radiating/invisible, we investigate the geometrical characterizationfor the underlying sources at polyhedral and conical corner. It is revealed thatthe non-radiating source with Hölder continuous regularity must vanish atthe corner. Using this kind of geometrical characterization of non-radiatingsources, we establish local and global unique determination for a source withthe polyhedral or corona shape support by a single far field measurement.Uniqueness by a single far field measurement constitutes of a long standingproblem in inverse scattering problems.
Keywords: Non-radiating sources; corner singularity; vanishing; inverse scattering; single far-field measurement.