WIAS Preprint No. 2242, (2016)

Acoustic scattering from corners, edges and circular cones



Authors

  • Elschner, Johannes
  • Hu, Guanghui

2010 Mathematics Subject Classification

  • 35R30 78A46

Keywords

  • inverse medium scattering, Helmholtz equation, non-scattering wavenumbers

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 non-convex. We prove that such an obstacle scatters any incoming wave non-trivially (i.e., 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 a 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.

Appeared in

  • Arch. Ration. Mech. Anal., 228:2 (2018) pp. 653--690.

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