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Integral equation methods in obstacle elastic scattering. (English) Zbl 1286.74055

Summary: The far-field equations for the rigid body, the cavity and the transmission case in two-dimensional linear elasticity are considered. In each case the corresponding far-field scattering amplitudes are presented. The direct scattering problem is formulated in differential and integral form. The boundary integral equations which are constructed using a layer theoretic approach and in particular a combination of single and double layer potentials are uniquely solvable. Assuming that the incident field is produced by a superposition of plane incident waves in all directions of propagation and polarization, it is proved that the scattered field is also expressed as the superposition of the corresponding scattered fields. A pair of integral equations of the first kind which hold independently of the boundary conditions are constructed in the far-field region. Properties of Herglotz functions are used to derive solvability conditions for the far-field equations.

MSC:

74J20 Wave scattering in solid mechanics
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