UNIQUENESS OF THE INVERSE TRANSMISSION SCATTERING WITH A CONDUCTIVE BOUNDARY CONDITION

• 作者: Jianli XIANG Guozheng YAN
• 来源期刊: 数学物理学报（英文版）
• 年，卷（期）: 2021,（3）
• 页码范围: 925-940
• 页数: 16页
• 语种: 英文
• DOI: 10.3969/j.issn.0252-9602.2021.03.018

摘要

This paper considers the inverse acoustic wave scattering by a bounded penetra-ble obstacle with a conductive boundary condition.We will show that the penetrable scatterer can be uniquely determined by its far-field pattern of the scattered field for all incident plane waves at a fixed wave number.In the first part of this paper,adequate preparations for the main uniqueness result are made.We establish the mixed reciprocity relation between the far-field pattern corresponding to point sources and the scattered field corresponding to plane waves.Then the well-posedness of a modified interior transmission problem is deeply investigated by the variational method.Finally,the a priori estimates of solutions to the general transmission problem with boundary data in Lp(?Ω)(1＜p＜2)are proven by the boundary integral equation method.In the second part of this paper,we give a novel proof on the uniqueness of the inverse conductive scattering problem.