Direct and inverse scalar scattering problems for the Helmholtz equation in R m

被引：4
|
作者：
Smirnov, Yury G. [1 ]
Tsupak, Aleksei A. [1 ]
机构：
[1] Penza State Univ, Dept Math & Supercomp, 40 Krasnaya St, Penza 440026, Russia
来源：
JOURNAL OF INVERSE AND ILL-POSED PROBLEMS | 2022年 / 30卷 / 01期
基金：
俄罗斯基础研究基金会;
关键词：
Helmholtz equations; boundary value problem; integral equation; unique solution;
D O I：
10.1515/jiip-2020-0060
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The boundary value problem for the Helmholtz equation in the m-dimensional free space is considered. The problem is reduced to the Lippmann-Schwinger integral equation over the inhomogeneity domain. The operator of the integral equation is shown to be an invertible Fredholm operator. The inverse coefficient problem is considered. An application of the two-step method reduces the inverse problem to the source-type integral equation with a smooth kernel. Special classes of solutions to this equation are introduced. The uniqueness of a solution to the integral equation of the first kind is proved in the defined function classes.
引用
收藏
页码：101 / 116
页数：16
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