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- ItemUniqueness in determining polyhedral sound-hard obstacles with a single incoming wave(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Elschner, Johannes; Yamamoto, MasahiroWe consider the inverse acoustic scattering problem of determining a sound-hard obstacle by far field measurements. It is proved that a polyhedral scatterer in $R^n, nge 2$, consisting of finitely many solid polyhedra, is uniquely determined by a single incoming plane wave.
- ItemUniqueness in inverse elastic scattering with finitely many incident waves(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Elschner, Johannes; Yamamoto, MasahiroWe consider the third and fourth exterior boundary value problems of linear isotropic elasticity and present uniqueness results for the corresponding inverse scattering problems with polyhedral-type obstacles and a finite number of incident plane elastic waves. Our approach is based on a reflection principle for the Navier equation.
- ItemUniqueness in inverse elastic scattering from unbounded rigid surfaces of rectangular type(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Elschner, Johannes; Hu, Guanghui; Yamamoto, MasahiroConsider the two-dimensional inverse elastic scattering problem of recovering a piecewise linear rigid rough or periodic surface of rectangular type for which the neighboring line segments are always perpendicular.We prove the global uniqueness with at most two incident elastic plane waves by using near-field data. If the Lamé constants satisfy a certain condition, then the data of a single plane wave is sufficient to imply the uniqueness. Our proof is based on a transcendental equation for the Navier equation, which is derived from the expansion of analytic solutions to the Helmholtz equation. The uniqueness results apply also to an inverse scattering problem for non-convex bounded rigid bodies of rectangular type.