论文标题
从麦克斯韦系统的广义阻抗边缘角和应用到反问题的独特延续
Unique continuation from a generalized impedance edge-corner for Maxwell's system and applications to inverse problems
论文作者
论文摘要
我们考虑具有广义阻抗边缘角的域中的时谐麦克斯韦系统，即存在两个在边缘处的普遍阻抗平面。阻抗参数可以为$ 0，\ infty $，也可以是有限的非相同消失的可变功能。我们在麦克斯韦系统的消失顺序与边缘角的二面角之间建立了准确的关系。特别是，如果角度是非理性的，则消失的顺序是无穷大的，即从边缘角度保持强大的独特延续。这些新的定量结果的建立涉及一个高度复杂且微妙的代数论点。我们对长期存在的逆电磁散射问题的研究强烈激励了独特的延续研究。作为一个重要的应用，我们得出了几种新颖的唯一可识别能力，从而通过单个远场测量来确定多面体障碍物及其表面阻抗。我们还讨论了我们的结果在与信息编码有关的反向散射理论中的另一个潜力和有趣的应用。
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 $0, \infty$ 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.
