Unique continuation from a generalized impedance edge-corner for Maxwell's system and applications to inverse problems. (8th February 2021)

• Record Type: Journal Article
• Authors: Diao, Huaian; Liu, Hongyu; Zhang, Long; Zou, Jun
• Is Part Of: Inverse problems. Volume 37:Number 3(2021)
• Publication Date: 2021-02-08
• Subjects: Maxwell's system -- generalized impedance plane -- edge-corner -- vanishing order -- inverse electromagnetic scattering -- single far-field measurement; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/abdb42
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We consider the time-harmonic Maxwell system in a domain with a generalized impedance edge-corner, namely the presence of two generalized impedance planes that intersect at an edge. The impedance parameter can be 0, ∞ or a finite non-identically vanishing function. We establish an accurate relationship between the vanishing order of the solutions to the Maxwell system and the dihedral angle of the edge-corner. In particular, if the angle is irrational, the vanishing order is infinity, i.e. strong unique continuation holds from the edge-corner. The establishment of those new quantitative results involve a highly intricate and subtle algebraic argument. The unique continuation study is strongly motivated by our study of a longstanding inverse electromagnetic scattering problem. As a significant application, we derive several novel unique identifiability results in determining a polyhedral obstacle as well as its surface impedance by a single far-field measurement. We also discuss another potential and interesting application of our result in the inverse scattering theory related to the information encoding.