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

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

数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (4): 1281-1297.doi: 10.1016/S0252-9602(12)60099-X

• 论文 • 下一篇

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

刘晓东|张波

LSEC and Institute of Applied Mathematics, AMSS, Chinese Academy of Sciences, Beijing 100190, China

收稿日期:2010-10-15 修回日期:2011-07-15 出版日期:2012-07-20 发布日期:2012-07-20
基金资助:
The work of the first author (XL) was supported by the China Postdoctoral Science Foundation (20100480494) the NSF of China (11101412) and K.C. Wong Education Foundation, Hong Kong. The work of the second author (BZ) was supported by the NSF of China (11071244,
11161130002).

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

LIU Xiao-Dong, ZHANG Bo

LSEC and Institute of Applied Mathematics, AMSS, Chinese Academy of Sciences, Beijing 100190, China

Received:2010-10-15 Revised:2011-07-15 Online:2012-07-20 Published:2012-07-20
Supported by:
The work of the first author (XL) was supported by the China Postdoctoral Science Foundation (20100480494) the NSF of China (11101412) and K.C. Wong Education Foundation, Hong Kong. The work of the second author (BZ) was supported by the NSF of China (11071244,
11161130002).

摘要/Abstract

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 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.

关键词: uniqueness, piecewise homogeneous medium, penetrable obstacle, unique continuation principle, Holmgrens uniqueness theorem, inverse scattering

Abstract:

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

中图分类号:

35P25

刘晓东, 张波. INVERSE SCATTERING BY AN INHOMOGENEOUS PENETRABLE OBSTACLE IN A PIECEWISE HOMOGENEOUS MEDIUM[J]. 数学物理学报(英文版), 2012, 32(4): 1281-1297.

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

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

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