Recovering the boundary corrosion from electrical potential distribution using partial boundary data

Jijun Liu Southeast University Gen Nakamura Inha University

Analysis of PDEs mathscidoc:2103.03004

Inverse Problems and Imaging, 11, (3), 521-538, 2017.4
We study detecting a boundary corrosion damage in the inaccessible part of a rectangular shaped electrostatic conductor from a one set of Cauchy data speci ed on an accessible boundary part of conductor. For this nonlinear ill-posed problem, we prove the uniqueness in a very general framework. Then we establish the conditional stability of Holder type based on some a priori assumptions on the unknown impedance and the electrical current input speci ed in the accessible part. Finally a regularizing scheme of double regularizing parameters, using the truncation of the series expansion of the solution, is proposed with the convergence analysis on the explicit regularizing solution in terms of a practical average norm for measurement data.
Electrical potential, Laplace equation, boundary impedance, regularization
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@inproceedings{jijun2017recovering,
  title={Recovering the boundary corrosion from electrical potential distribution using partial boundary data},
  author={Jijun Liu, and Gen Nakamura},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210325171743002741764},
  booktitle={Inverse Problems and Imaging},
  volume={11},
  number={3},
  pages={521-538},
  year={2017},
}
Jijun Liu, and Gen Nakamura. Recovering the boundary corrosion from electrical potential distribution using partial boundary data. 2017. Vol. 11. In Inverse Problems and Imaging. pp.521-538. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210325171743002741764.
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