Journal article
Solving a nonlinear inverse Robin problem through a linear Cauchy problem
Applicable analysis, Vol.99(12), pp.2093-2114
09/09/2020
DOI: 10.1080/00036811.2018.1553037
Abstract
Considered in this paper is an inverse Robin problem governed by a steady-state diffusion equation. By the Robin inverse problem, one wants to recover the unknown Robin coefficient on an inaccessible boundary from Cauchy data measured on the accessible boundary. In this paper, instead of reconstructing the Robin coefficient directly, we compute first the Cauchy data on the inaccessible boundary which is a linear inverse problem, and then compute the Robin coefficient through Newton's law. For the Cauchy problem, a parameter-dependent coupled complex boundary method (CCBM) is applied. The CCBM has its own merits, and this is particularly true when it is applied to the Cauchy problem. With the introduction of a positive parameter, we can prove the regularized solution is uniformly bounded with respect to the regularization parameter which is a very good property because the solution can now be reconstructed for a rather small value of the regularization parameter. For the problem of computing the Robin coefficient from the recovered Cauchy data, a least square output Tikhonov regularization method is applied to Newton's law to obtain a stable approximate Robin coefficient. Numerical results are given to show the feasibility and effectiveness of the proposed method.
Details
- Title: Subtitle
- Solving a nonlinear inverse Robin problem through a linear Cauchy problem
- Creators
- R. F Gong - Nanjing University of Aeronautics and AstronauticsP. J Yu - Nanjing University of Aeronautics and AstronauticsQ. N Jin - Australian National UniversityX. L Cheng - Zhejiang UniversityW Han - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Applicable analysis, Vol.99(12), pp.2093-2114
- Publisher
- TAYLOR & FRANCIS LTD
- DOI
- 10.1080/00036811.2018.1553037
- ISSN
- 0003-6811
- eISSN
- 1563-504X
- Number of pages
- 22
- Grant note
- 11401304; 11571311 / Natural Science Foundation of China FT170100231 / Australian Research Council
- Language
- English
- Date published
- 09/09/2020
- Academic Unit
- Mathematics
- Record Identifier
- 9984240773402771
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