Interface with weakly singular points always scatter. (8th May 2018)

• Record Type: Journal Article
• Authors: Li, Long; Hu, Guanghui; Yang, Jiansheng
• Is Part Of: Inverse problems. Volume 34:Number 7(2018:Jul.)
• Publication Date: 2018-05-08
• Subjects: uniqueness -- inverse medium scattering -- non-scattering energy -- weakly singular corners -- Helmholtz equation; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aabe56
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: Assume that a bounded scatterer is embedded into an infinite homogeneous isotropic background medium in two dimensions. The refractive index function is supposed to be piecewise constant. If the scattering interface contains a weakly singular point, we prove that the scattered field cannot vanish identically. This implies the absence of non-scattering energies for piecewise analytic interfaces with one singular point. Local uniqueness is obtained for shape identification problems in inverse medium scattering with a single far-field pattern.