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- Title
Acoustic Scattering from Corners, Edges and Circular Cones.
- Authors
ELSCHNER, JOHANNES; GUANGHUI HU
- 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, 2π)\{π}. 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.
- Subjects
SOUND wave scattering; CONES; EDGES (Geometry); UNIQUENESS (Mathematics); WAVENUMBER; LAPLACE'S equation
- Publication
Archive for Rational Mechanics & Analysis, 2018, Vol 228, Issue 2, p653
- ISSN
0003-9527
- Publication type
Academic Journal
- DOI
10.1007/s00205-017-1202-4