Open Access
FALL 2013 Reconstruction for cavities with impedance boundary condition
Hai-Hua Qin, Ji-Chuan Liu
J. Integral Equations Applications 25(3): 431-454 (FALL 2013). DOI: 10.1216/JIE-2013-25-3-431


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.


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Hai-Hua Qin. Ji-Chuan Liu. "Reconstruction for cavities with impedance boundary condition." J. Integral Equations Applications 25 (3) 431 - 454, FALL 2013.


Published: FALL 2013
First available in Project Euclid: 16 December 2013

zbMATH: 06243001
MathSciNet: MR3161621
Digital Object Identifier: 10.1216/JIE-2013-25-3-431

Primary: 35J25 , 45Q05 , 65R30 , 78A46

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

Rights: Copyright © 2013 Rocky Mountain Mathematics Consortium

Vol.25 • No. 3 • FALL 2013
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