Retrieving the Robin coefficient from single Cauchy data in elliptic systems

: pp. 663–677
Received: February 16, 2022
Revised: July 04, 2022
Accepted: July 05, 2022
Faculty of Sciences and Techniques, Department of Mathematics and Informatics LAMAI, Cadi Ayyad University, Marrakech, Morocco
Faculty of Sciences and Techniques, Department of Mathematics and Informatics LAMAI, Cadi Ayyad University, Marrakech, Morocco

The purpose of this work is to identify a Robin coefficient from available measurements on the accessible part of the boundary.  After recasting the inverse problem as an optimization problem, we study the issue of identifiability, stability, and identification.  For the reconstruction process, two regularized algorithms are designed, and the forward problem is approximated using the discontinuous dual reciprocity method.  The accuracy of the proposed approaches is tested in the case of noise–free and noisy data and the findings are very promising and encouraging.

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Mathematical Modeling and Computing, Vol. 9, No. 3, pp. 663–677 (2022)