2016/10/11 by Genqian Liu, Liu, Genqian
Engineering · Mathematics · Physics and Astronomy · #35J05 #35P25 #35R30 #78A46 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Microwave Imaging and Scattering Analysis #Numerical methods in inverse problems #Ultrasonics and Acoustic Wave Propagation #math-ph #math.AP #math.MP #msc:35J05 #msc:35P25 #msc:35R30 #msc:78A46
paper · pdf · doi:10.48550/arxiv.1610.03237
The proof of main theorem in this paper has a gap
openalex publication_date 2016/10/11 · arxiv created 2021/04/18 · arxiv updated 2021/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we give a positive answer to a challenging open problem for recovering unknown obstacle (which is usually referred to as a scatterer) by acoustic wave probe associated to the Helmholtz equation. We show that the acoustic scattering amplitude A(β, α0, k0), known for all β∈ \mathbb S2, where \mathbb S2 is the unit sphere in ℝ3, α0∈ \mathbbS2 is fixed, k0>0 is fixed, determines the obstacle D and the boundary condition on ∂ D uniquely (The boundary condition on ∂ D is either the Dirichlet, or Neumann, or the impedance one).