RECOVERING THE IMPEDANCE FUNCTION OR SHAPE OF ELASTIC OBSTACLE FROM PARTIAL CAUCHY DATA

被引：0

作者：

Sun, Yao ^{[1
]}

Wang, Pan ^{[1
]}

Chen, Bo ^{[1
]}

机构：

[1] Civil Aviat Univ China, Coll Sci, Tianjin 300300, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2024年 / 17卷 / 08期

关键词：

Inverse impedance problem; inverse shape problem; Cauchy data; boundary integral equation; Navier equation; FINITE-ELEMENT-METHOD; STABLE DETERMINATION; SCATTERING PROBLEMS; WAVE SCATTERING; SAMPLING METHOD; MODIFIED BEM; RECONSTRUCTION; EQUATIONS; CAVITIES;

D O I：

10.3934/dcdss.2024025

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we focus on recovering the impedance function or the boundary shape from a pair of Cauchy data on the known boundary by using an indirect boundary integral equation. This present problem has been divided into two parts. The first part is to solve a Cauchy problem through using an indirect boundary integral equation method combining a regularization technique. Then, the elastic impedance function is given by a point to point method. The second part is to recover the elastic shape by a Newton -type iterative method. The effectiveness of the method has been shown by solving some examples.

引用

页码：2654 / 2678

页数：25

共 50 条

[1] Recovering an obstacle and its impedance from Cauchy data
Rundell, William
INVERSE PROBLEMS, 2008, 24 (04)
[2] Recovering an obstacle and a nonlinear conductivity from Cauchy data
Rundell, William
INVERSE PROBLEMS, 2008, 24 (05)
[3] Recovering source location, polarization, and shape of obstacle from elastic scattering data
Chang, Yan
Guo, Yukun
Liu, Hongyu
Zhang, Deyue
JOURNAL OF COMPUTATIONAL PHYSICS, 2023, 489
[4] Recovering a potential from partial Cauchy data
Bukhgeim, AL
Uhlmann, G
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2002, 27 (3-4) : 653 - 668
[5] Shape reconstruction for an inverse biharmonic problem from partial Cauchy data
Bouslah, Zineb
Hadj, Abdelhak
Saker, Hacene
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2024, 47 (03) : 1613 - 1627
[6] Simultaneous reconstruction of the shape and surface impedance from Cauchy data for the Helmholtz equation
Liu, Ji-Chuan
OPTIMIZATION, 2024,
[7] Interior Elastic Scattering by a Non-Penetrable Partially Coated Obstacle and Its Shape Recovering
Kaiafa, Angeliki
Sevroglou, Vassilios
MATHEMATICS, 2021, 9 (19)
[8] ON THE DATA COMPLETION PROBLEM AND THE INVERSE OBSTACLE PROBLEM WITH PARTIAL CAUCHY DATA FOR LAPLACE'S EQUATION
Caubet, Fabien
Darde, Jeremi
Godoy, Matias
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2019, 25
[9] Recovering Simultaneously a Potential and a Point Source from Cauchy Data
Bao, Gang
Liu, Yuantong
Triki, Faouzi
MINIMAX THEORY AND ITS APPLICATIONS, 2021, 6 (02): : 227 - 238
[10] Jointly determining the point sources and obstacle from Cauchy data
Zhang, Deyue
Chang, Yan
Guo, Yukun
INVERSE PROBLEMS, 2024, 40 (01)

← 1 2 3 4 5 →