Liu, Xiaodong; Zhang, Bo Direct and inverse obstacle scattering problems in a piecewise homogeneous medium. (English) Zbl 1211.35213 SIAM J. Appl. Math. 70, No. 8, 3105-3120 (2010). 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. Cited in 19 Documents 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 Keywords:uniqueness; piecewise homogeneous medium; acoustic; Holmgren’s uniqueness theorem; inverse scattering PDFBibTeX XMLCite \textit{X. Liu} and \textit{B. Zhang}, SIAM J. Appl. Math. 70, No. 8, 3105--3120 (2010; Zbl 1211.35213) Full Text: DOI arXiv