長沙理工大學學術活動預告
報告承辦單位: 數學與統計學院
報告題目: Uniqueness to inverse grating diffraction problem with infinitely many plane waves
報告內容:
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.
報告人姓名: 徐小緒
報告人所在單位: 北京計算科學研究中心
報告人職稱/職務及學術頭銜: 博士后
報告時間: 2020年10月29日16:25－17:10
報告方式: 理科樓A-419
報告人簡介: 徐小緒博士2019年獲中國科學院大學博士學位，現今在北京計算科學研究中心開展博士后研究，研究興趣為聲波與電磁波無相位反散射問題的理論與算法。目前正承擔1項中國博士后科學基金項目，已發表SCI論文5篇。