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报告承办单位: 数学与统计学院

报告题目:  Uniqueness to inverse grating diffraction problem with infinitely many plane waves

报告内容:  

In this talk, we focus on the inverse grating diffraction problem in two dimensional case. We prove that a sound-soft periodic curve can be uniquely determined by the near-field data incited by infinitely many incident plane waves with distinct directions at a fixed frequency. Our proof is based on Schiffer’s idea that the total fields for distinct incident directions are linearly independent and for a fixed wave number there exist only finitely many linearly independent Dirichlet eigenfunctions in a bounded domain or a periodic strip under some assumptions on the surface. And based on the Rayleigh expansion for the scattered field we also prove that the phased near-field data can be uniquely determined by the phaseless near-field data in a bounded domain except a finite set of incident angles. Our proof is also valid for periodic surfaces with other boundary conditions. As a direct corollary, the corresponding uniqueness result for inverse sound-soft periodic surface scattering problem based on phaseless near-field data in a bounded domain can be established.

报告人姓名:  徐小绪

报告人所在单位: 北京计算科学研究中心

报告人职称/职务及学术头衔:    博士后

报告时间:  2020年10月29日16:25－17:10

报告方式: 理科楼A-419 

报告人简介:  徐小绪博士2019年获中国科学院大学博士学位，现今在北京计算科学研究中心开展博士后研究，研究兴趣为声波与电磁波无相位反散射问题的理论与算法。目前正承担1项中国博士后科学基金项目，已发表SCI论文5篇。