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Zbl 1180.35569
Liu, Xiaodong; Zhang, Bo; Hu, Guanghui
Uniqueness in the inverse scattering problem in a piecewise homogeneous medium. (English)
[J] Inverse Probl. 26, No. 1, Article ID 015002, 14 p. (2010). ISSN 0266-5611

Summary: The scattering of time-harmonic acoustic plane waves by an impenetrable obstacle in a piecewise homogeneous medium is considered. Having established the well posedness of the direct problem by the variational method, we prove a uniqueness result for the inverse problem, that is, the unique determination of the obstacle and its boundary condition from a knowledge of the far-field pattern for incident plane waves. The proof is based on a generalization of the mixed reciprocity relation.

MSC 2000:: *35R30 Inverse problems for PDE
78A46 Inverse scattering problems
78A48 optics in special media
76Q05 Density waves (fluid mechanics)
35J05 Laplace equation, etc.

Keywords: Helmholtz equation; Dirichlet to Neumann operator; acoustic plane waves

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