2020/05/13 by Huaian Diao, Hongyu Liu, Diao, Huaian +5
Engineering · Mathematics · Physics and Astronomy · #Electromagnetic Scattering and Analysis #Microwave Imaging and Scattering Analysis #Numerical methods in inverse problems #math.AP #msc:35P05 #msc:35P25 #msc:35Q60 #msc:35R30
paper · pdf · doi:10.48550/arxiv.2005.06352
arxiv created 2020/05/14 · arxiv updated 2020/05/15
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 variable 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 it 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.