On well-posedness of scattering problems in a kirchhoff–love infinite plate

Laurent Bourgeois; Christophe Hazard

doi:10.1137/19M1295660

On well-posedness of scattering problems in a kirchhoff–love infinite plate

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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).

Original language	English
Pages (from-to)	1546-1566
Number of pages	21
Journal	SIAM Journal on Applied Mathematics
Volume	80
Issue number	3
DOIs	https://doi.org/10.1137/19M1295660
Publication status	Published - 1 Jan 2020

Keywords

Bi-Laplacian operator
Dirichlet-to-Neumann map
Radiation condition

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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).",

keywords = "Bi-Laplacian operator, Dirichlet-to-Neumann map, Radiation condition",

author = "Laurent Bourgeois and Christophe Hazard",

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AU - Hazard, Christophe

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N2 - 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).

AB - 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).

KW - Bi-Laplacian operator

KW - Dirichlet-to-Neumann map

KW - Radiation condition

U2 - 10.1137/19M1295660

DO - 10.1137/19M1295660

M3 - Article

AN - SCOPUS:85093087890

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VL - 80

SP - 1546

EP - 1566

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

IS - 3

ER -

On well-posedness of scattering problems in a kirchhoff–love infinite plate

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Keywords

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