Filters

2010 - 20122

More filters

20192
Reset filters

Settings

Author: Hu, Guanghui × End date: 2013 × Start date: 2010 × DDC: 510 × Subject: Elastic waves × Subject: variational formulation × WGL Institute: WIAS ×

Search Results

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Elastic scattering by unbounded rough surfaces
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Elschner, Johannes; Hu, Guanghui
    We consider the two-dimensional time-harmonic elastic wave scattering problem for an unbounded rough surface, due to an inhomogeneous source term whose support lies within a finite distance above the surface. The rough surface is supposed to be the graph of a bounded and uniformly Lipschitz continuous function, on which the elastic displacement vanishes. We propose an upward propagating radiation condition (angular spectrum representation) for solutions of the Navier equation in the upper half-space above the rough surface, and establish an equivalent variational formulation. Existence and uniqueness of solutions at arbitrary frequency is proved by applying a priori estimates for the Navier equation and perturbation arguments for semi-Fredholm operators.
  • Thumbnail Image
    Item
    Scattering of plane elastic waves by three-dimensional diffraction gratings
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Elschner, Johannes; Hu, Guanghui
    The reflection and transmission of a time-harmonic plane wave in an isotropic elastic medium by a three-dimensional diffraction grating is investigated. If the diffractive structure involves an impenetrable surface, we study the first, second, third and fourth kind boundary value problems for the Navier equation in an unbounded domain by the variational approach. Based on the Rayleigh expansions, a radiation condition for quasi-periodic solutions is proposed. Existence of solutions in Sobolev spaces is established if the grating profile is a two dimensional Lipschitz surface, while uniqueness is proved only for small frequencies or for all frequencies excluding a discrete set. Similar solvability results are obtained for multilayered transmission gratings in the case of an incident pressure wave. Moreover, by a periodic Rellich identity, uniqueness of the solution to the first kind (Dirichlet) boundary value problem is established for all frequencies under the assumption that the impenetrable surface is given by the graph of a Lipschitz function