2020/10/02 by Long Li, Guanghui Hu, Li, Long +3 · 2 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Microwave Imaging and Scattering Analysis #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2010.00748
openalex publication_date 2020/10/02 · openalex created_date 2020/10/08 · openalex updated_date 2026/07/28
It is proved that an inhomogeneous medium whose boundary contains a weakly singular point of arbitrary order scatters every incoming wave. Similarly, a compactly supported source term with weakly singular points on the boundary always radiates acoustic waves. These results imply the absence of non-scattering energies and non-radiating sources in a domain that is not C^∞-smooth. Local uniqueness results with a single far-field pattern are obtained for inverse source and inverse medium scattering problems. Our arguments provide a sufficient condition of the surface under which solutions to the Helmholtz equation admits no analytical continuation.