Abstract
Consider the time-harmonic acoustic scattering from a bounded penetrable obstacle imbedded in an isotropic homogeneous medium. The obstacle is supposed to possess a circular conic point or an edge point on the boundary in three dimensions and a planar corner point in two dimensions. The opening angles of cones and edges are allowed to be any number in \({(0,2\pi)\backslash\{\pi\}}\). We prove that such an obstacle scatters any incoming wave non-trivially (that is, the far field patterns cannot vanish identically), leading to the absence of real non-scattering wavenumbers. Local and global uniqueness results for the inverse problem of recovering the shape of penetrable scatterers are also obtained using a single incoming wave. Our approach relies on the singularity analysis of the inhomogeneous Laplace equation in a cone.
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Communicated by N. Masmoudi
The work of G. Hu is supported by the NSFC Grant (No. 11671028), NSAF Grant (No. U1530401) and the 1000-Talent Program of Young Scientists in China.
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Elschner, J., Hu, G. Acoustic Scattering from Corners, Edges and Circular Cones. Arch Rational Mech Anal 228, 653–690 (2018). https://doi.org/10.1007/s00205-017-1202-4
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DOI: https://doi.org/10.1007/s00205-017-1202-4