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Direct and inverse obstacle scattering problems in a piecewise homogeneous medium. (English) Zbl 1211.35213

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:

35P25 Scattering theory for PDEs
35R30 Inverse problems for PDEs
35B45 A priori estimates in context of PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory
78A48 Composite media; random media in optics and electromagnetic theory
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