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Zbl 1211.35213
Liu, Xiaodong; Zhang, Bo
Direct and inverse obstacle scattering problems in a piecewise homogeneous medium. (English)
[J] SIAM J. Appl. Math. 70, No. 8, 3105-3120 (2010). ISSN 0036-1399; ISSN 1095-712X/e

Summary: This paper is concerned with the problem of scattering of time-harmonic acoustic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is established, employing the integral equation method, and then used, in conjunction with the representation in a combination of layer potentials of the solution, to prove a priori estimates of solutions on some part of the interface between the layered media. The inverse problem is also considered in this paper. A uniqueness result is obtained for the first time in determining both the penetrable interface and the impenetrable obstacle with its physical property from a knowledge of the far field pattern for incident plane waves. In doing so, an important role is played by the a priori estimates of the solution for the direct problem.

MSC 2000:: *35P25 Scattering theory (PDE)
35R30 Inverse problems for PDE
35B45 A priori estimates
35J05 Laplace equation, etc.
78A46 Inverse scattering problems
78A48 optics in special media

Keywords: uniqueness; piecewise homogeneous medium; acoustic; Holmgren's uniqueness theorem; inverse scattering

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