On the reconstruction of boundary impedance of a heat conduction system from nonlocal measurement

Jijun Liu Southeast University Yuchan Wang Southeast University

Numerical Analysis and Scientific Computing mathscidoc:2103.25009

Inverse Problems, 32, (7), 075002, 2016.7
We consider the reconstruction of the Robin impedance coefficient of a heat conduction system in a two-dimensional spatial domain from the time-average measurement specified on the boundary. By applying the potential representation of a solution, this nonlinear inverse problem is transformed into an ill-posed integral system coupling the density function for potential and the unknown boundary impedance. The uniqueness as well as the conditional stability of this inverse problem is established from the integral system. Then we propose to find the boundary impedance by solving a non-convex regularizing optimization problem. The well-posedness of this optimization problem together with the convergence property of the minimizer is analyzed. Finally, based on the singularity decomposition of the potential representation of the solution, two iteration schemes with their numerical realizations are proposed to solve this optimization problem
inverse problem, heat equation, robin coefficient, uniqueness, optimization
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@inproceedings{jijun2016on,
  title={On the reconstruction of boundary impedance of a heat conduction system from nonlocal measurement},
  author={Jijun Liu, and Yuchan Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210325180330227121769},
  booktitle={Inverse Problems},
  volume={32},
  number={7},
  pages={075002},
  year={2016},
}
Jijun Liu, and Yuchan Wang. On the reconstruction of boundary impedance of a heat conduction system from nonlocal measurement. 2016. Vol. 32. In Inverse Problems. pp.075002. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210325180330227121769.
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