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The inverse scattering problem by a crack buried in a piecewise homogeneous medium. (English) Zbl 1330.35436
Summary: This paper is concerned with the inverse scattering problem of time-harmonic acoustic plane waves by a crack buried in a piecewise homogeneous medium. We first show the well-posedness of the solution to the direct problem by using the boundary integral method. Then a uniqueness result for the inverse problem is obtained, that is, the shape of the crack and the surface parameter can be uniquely determined by the far-field pattern. The proof of the uniqueness result is based on a generalization of the mixed reciprocity relation. In particular, a mathematical basis is given to retrieve the shape of the crack by using the linear sampling method and difficulties arise from the fact that the crack has an empty interior.

MSC:
35Q74 PDEs in connection with mechanics of deformable solids
74J20 Wave scattering in solid mechanics
74J25 Inverse problems for waves in solid mechanics
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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