INVERSE SCATTERING BY AN INHOMOGENEOUS PENETRABLE OBSTACLE IN A PIECEWISE HOMOGENEOUS MEDIUM

doi:10.1016/S0252-9602(12)60099-X

Abstract

Abstract:

This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using the in-tegral equation method. We then proceed to establish two tools that play important roles for the inverse problem: one is a mixed reciprocity relation and the other is a priori esti-mates of the solution on some part of the interfaces between the layered media. For the inverse problem, we prove in this paper that both the penetrable interfaces and the possible inside inhomogeneity can be uniquely determined from a knowledge of the far field pattern for incident plane waves.

Key words: uniqueness, piecewise homogeneous medium, penetrable obstacle, unique continuation principle, Holmgrens uniqueness theorem, inverse scattering

CLC Number:

35P25

LIU Xiao-Dong, ZHANG Bo. INVERSE SCATTERING BY AN INHOMOGENEOUS PENETRABLE OBSTACLE IN A PIECEWISE HOMOGENEOUS MEDIUM[J].Acta mathematica scientia,Series B, 2012, 32(4): 1281-1297.

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