Journal of Integral Equations and Applications

Reconstruction for cavities with impedance boundary condition

Hai-Hua Qin and Ji-Chuan Liu

Full-text: Open access

Abstract

In this paper, we consider the inverse scattering problem of recovering the shape of a cavity or the surface impedance from one source and a knowledge of measurements placed on a curve inside the cavity. Based on a potential approach the inverse problem is equivalent to a system of nonlinear and ill-posed integral equations, a regularized Newton iterative approach is applied to reconstruct the boundary and the injectivity for the linearized system is established. Numerical examples are provided showing the viability of our method.

Article information

Source
J. Integral Equations Applications, Volume 25, Number 3 (2013), 431-454.

Dates
First available in Project Euclid: 16 December 2013

Permanent link to this document
https://projecteuclid.org/euclid.jiea/1387207806

Digital Object Identifier
doi:10.1216/JIE-2013-25-3-431

Mathematical Reviews number (MathSciNet)
MR3161621

Zentralblatt MATH identifier
06243001

Subjects
Primary: 35J25: Boundary value problems for second-order elliptic equations 45Q05: Inverse problems 65R30: Improperly posed problems 78A46: Inverse scattering problems

Keywords
Inverse scattering problem shape of a cavity surface impedance potential approach nonlinear integral equations

Citation

Qin, Hai-Hua; Liu, Ji-Chuan. Reconstruction for cavities with impedance boundary condition. J. Integral Equations Applications 25 (2013), no. 3, 431--454. doi:10.1216/JIE-2013-25-3-431. https://projecteuclid.org/euclid.jiea/1387207806


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