Inverse scattering by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium

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• 作者：Liu Xiaodong ^{xdliu@amt.ac.cn} ; Zhang Bo ^{b.zhang@amt.ac.cn}
• 关键词：uniqueness ; piecewise homogeneous medium ; penetrable obstacle ; unique continuation principle ; Holmgrenl's uniqueness theorem ; inverse scattering
• 刊名：Acta Mathematica Scientia
• 出版年：2012
• 期刊代码：1_02529602
• 类别：mt
• 出版时间：July, 2012
• 卷：32
• 期：4
• 页码：1281-1297
• 文件大小：757 K

摘要

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 integral 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 estimates 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.