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Title: Elastic scattering by unbounded rough surfaces : solvability in weighted Sobolev spaces
Authors: Elschner, JohannesHu, Guanghui
Issue Date: 2013
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 1780, ISSN 0946-8633
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract: This paper is concerned with the variational approach in weighted Sobolev spaces to timeharmonic elastic scattering by two-dimensional unbounded rough surfaces. The rough surface is supposed to be the graph of a bounded and uniformly Lipschitz continuous function, on which the total elastic displacement satisfies either the Dirichlet or impedance boundary condition. We establish uniqueness and existence results for both elastic plane and point source (spherical) wave incidence, following the recently developed variational approach in [SIAM J. Math. Anal., 42: 6 (2010), pp. 2554 2580] for the Helmholtz equation. This paper extends our previous solvability results [SIAM J. Math. Anal., 44: 6 (2012), pp. 4101-4127] in the standard Sobolev space to the weighted Sobolev spaces.
Keywords: Non-smooth rough surface; linear elasticity; radiation condition; variational formulation; weighted Sobolev spaces; Navier equation
DDC: 510
License: This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
Appears in Collections:Mathematik

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