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Author: Elschner, Johannes × Subject: Helmholtz equation ×

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    Variational approach in weighted Sobolev spaces to scattering by unbounded rough surface
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Chandler-Wilde, Simon N.; Elschner, Johannes
    [no abstract available]
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    Corners and edges always scatter
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Elschner, Johannes; Hu, Guanghui
    Consider time-harmonic acoustic scattering problems governed by the Helmholtz equation in two and three dimensions. We prove that bounded penetrable obstacles with corners or edges scatter every incident wave nontrivially, provided the function of refractive index is real-analytic. Moreover, if such a penetrable obstacle is a convex polyhedron or polygon, then its shape can be uniquely determined by the far-field pattern over all observation directions incited by a single incident wave. Our arguments are elementary and rely on the expansion of solutions to the Helmholtz equation.