A FIXED ENERGY FIXED ANGLE INVERSE SCATTERING IN INTERIOR TRANSMISSION PROBLEM

被引：2

作者：

Chen, Lung-Hui ^{[1
]}

机构：

[1] Natl Chung Cheng Univ, Dept Math, Chiayi, Taiwan

来源：

REPORTS ON MATHEMATICAL PHYSICS | 2017年 / 79卷 / 03期

关键词：

inverse problem; inverse scattering; interior transmission eigenvalue; entire function theory; Rellich's lemma; Sturm Liouville problem; STURM-LIOUVILLE PROBLEMS; UNIQUENESS THEOREM; EIGENVALUES; OBSTACLE;

D O I：

10.1016/S0034-4877(17)30047-2

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We study the inverse acoustic scattering problem in mathematical physics. The problem is to recover the index of refraction in an inhomogeneous medium by measuring the scattered wave fields in the far field. We transform the problem to the interior transmission problem in the study of the Helmholtz equation. We find an inverse uniqueness on the scatterer with a knowledge of a fixed interior transmission eigenvalue. By examining the solution in a series of spherical harmonics in the far field, we can determine uniquely the perturbation source for the radially symmetric perturbations.

引用

页码：331 / 345

页数：15

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