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On the far-field operator in elastic obstacle scattering. (English) Zbl 1141.35429
We investigate the far-field operator for the scattering of time-harmonic elastic plane waves by either a rigid body, a cavity, or an absorbing obstacle. Extending results of Colton and Kress for acoustic obstacle scattering, for the spectrum of the far-field operator we show that there exist an infinite number of eigenvalues and determine disks in the complex plane where these eigenvalues lie. In addition, as counterpart of an identity in acoustic scattering due to Kress and Päivärinta, we will establish a factorization for the difference of the far-field operators for two different scatterers. Finally, extending a sampling method for the approximate solution of the acoustic inverse obstacle scattering problem suggested by Kirsch to elasticity, this factorization is used for a characterization of a rigid scatterer in terms of the eigenvalues and eigenelements of the far-field operator.

MSC:
35P25 Scattering theory for PDEs
35Q72 Other PDE from mechanics (MSC2000)
74J20 Wave scattering in solid mechanics
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