The far-field equations in linear elasticity -- an inversion scheme (Q2731089)
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scientific article; zbMATH DE number 1625533
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The far-field equations in linear elasticity -- an inversion scheme |
scientific article; zbMATH DE number 1625533 |
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2001
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wave scattering
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asymptotic methods
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series representations
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The far-field equations in linear elasticity -- an inversion scheme (English)
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An inverse scattering problem of three-dimensional homogeneous isotropic elastodynamics is discussed. First, a direct scattering problem for a cavity or a rigid body in \(E^3\) is formulated, and a far-field dyadic solution to the problem in terms of a free-space Green's function is obtained. Next, an inverse problem is formulated in which a shape of the scatterer is to be found using only longitudinal or transversal farfield data. A solution to the problem in terms of the Herglotz tensor functions [see \textit{G. Dassios} and \textit{Z. Rigou}, ibid. 77, 911--923 (1997; Zbl 0910.73017)] is proposed, and the case of a rigid spherical scatterer is discussed in detail.
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