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

作　　者：刘晓东 张波 

机构地区：[1]LSEC and Institute of Applied Mathematics,AMSS,Chinese Academy of Sciences,Beijing 100190,China

出　　处：《Acta Mathematica Scientia》2012年第4期1281-1297,共17页数学物理学报（B辑英文版）

基　　金：the first author (XL) was supported by the China Postdoctoral Science Foundation (20100480494);the NSF of China (11101412);K.C. Wong Education Foundation, Hong Kong;the second author (BZ) was supported by the NSF of China (11071244,11161130002)

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.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.

关 键 词：UNIQUENESS piecewise homogeneous medium penetrable obstacle uniquecontinuation principle Holmgren＇s uniqueness theorem inverse scattering 

分 类 号：O422.5[理学—声学] O175.5[理学—物理]