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Acoustic Scattering from Corners, Edges and Circular Cones

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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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Author information

Authors and Affiliations

  1. Weierstrass Institute, Mohrenstr. 39, 10117, Berlin, Germany

    Johannes Elschner

  2. Beijing Computational Science Research Center, Beijing, 100193, China

    Guanghui Hu

Authors
  1. Johannes Elschner
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  2. Guanghui Hu
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Corresponding author

Correspondence to Guanghui Hu.

Additional information

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

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