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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.
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