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On well-posedness of scattering problems in a Kirchhoff-Love infinite plate

Laurent Bourgeois 1 Christophe Hazard 1
1 POEMS-POST - Propagation des Ondes : Etude Mathématique et Simulation
UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique, Inria Saclay - Ile de France
Abstract : We address scattering problems for impenetrable obstacles in an infinite elastic Kirchhoff-Love two-dimensional plate. The analysis is restricted to the purely bending case and the time-harmonic regime. Considering four types of boundary conditions on the obstacle, well-posedness for those problems is proved with the help of a variational approach: (i) for any wave number k when the plate is clamped, simply supported or roller supported; (ii) for any k except a discrete set when the plate is free (this set is finite for convex obstacles).
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Laurent Bourgeois, Christophe Hazard. On well-posedness of scattering problems in a Kirchhoff-Love infinite plate. SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2020, 80 (3), pp.1546-1566. ⟨hal-02334004⟩

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