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Approximation de la diffraction d’ondes √©lastiques: Une nouvelle approche. (French) Zbl 0571.73020
Nonlinear partial differential equations and their applications, Coll. de France Semin., Paris 1982-83, Vol. VI, Res. Notes Math. 109, 48-95 (1984).
[For the entire collection see Zbl 0543.00005.]
This work treats the diffraction of waves in a linearized, isotropic, elastic space by a smooth boundary. The author extends to three dimensions results obtained by others in the two dimensional equations of elasticity. Proceeding from the representation of the diffracted wave by an integral equation involving an unknown density of displacement discontinuity on the diffracting object, the associated variational problem is shown to have a bilinear form whose kernel possesses a particularly simple Fourier transform. The proof of the representation is given in detail, and consists of reducting the general case to special geometries for which the calculation can be carried out explicitly.
Reviewer: J.L.Thompson

74J20 Wave scattering in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74B99 Elastic materials
45F99 Systems of linear integral equations