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This paper is concerned with the unique identification of the shape of ascatterer through a single far-field pattern in an inverse elastic mediumscattering problem with a generalized transmission boundary condition. Theuniqueness issue by a single far-field measurement is a challenging problem ininverse scattering theory, which has a long and colorful history. In thispaper, we demonstrate the well-posedness of the direct problem by thevariational approach. We establish the uniqueness results by a single far-fieldmeasurement under a generic scenario when dealing with underlying elasticscatterers exhibiting polygonal-nest or polygonal-cell structures. Furthermore,for a polygonal-nest or polygonal-cell structure scatterer associated withdensity and boundary impedance parameters as piecewise constants, we show thatthese physical quantities can be uniquely determined simultaneously by a singlefar-field measurement. The corresponding proof relies heavily on examining thesingular behaviour of a coupled PDE system near a corner in a microlocalmanner.

Unique determination by a single far-field measurement for an inverse elastic problem