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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:
35P25Scattering theory (PDE)
35R30Inverse problems for PDE
35B45A priori estimates for solutions of PDE
35J05Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
78A46Inverse scattering problems
78A48optics in special media