Abstract
The study of the paper mainly focuses on recovering the dissipative parameter in a coupled system formed by coupling a bilaplacian operator to a heat equation from final time measured output data via a quasi-solution approach with optimization. The inverse coefficient problem is expressed as a minimization problem. We establish the existence of a minimizer and extract the necessary optimality condition, which is essential in proving the requisite stability result for the inverse coefficient problem. The effectiveness of the proposed approach is demonstrated through an analysis of numerical results using the conjugate gradient approach.
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Acknowledgements
The authors thank Navaneetha Krishnan Karuppusamy, Central University of Tamil Nadu, India who initiated this work and for the help made in numerical section. The first author thank the University Grants Commission, India for the financial support via CSIR- UGC Junior Research Fellowship (UGC Ref. No.: 1198/(CSIR-UGC NET DEC. 2018)). The National Board for Higher Mathematics has funded the second author’s work with research grant (No.: 02011/13/2022/R &D-II/10206). The last author was supported by SERB through the research grant (No.: SR/FTP/MS-048/2011 dt. 23.06.2014). The authors thank the anonymous referees for their invaluable suggestions which improved the quality of this article.
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Murugesan, N.K., Sakthivel, K., Hasanov, A. et al. Inverse Coefficient Problem for the Coupled System of Fourth and Second Order Partial Differential Equations. Appl Math Optim 89, 74 (2024). https://doi.org/10.1007/s00245-024-10142-5
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DOI: https://doi.org/10.1007/s00245-024-10142-5
Keywords
- Inverse problems
- Quasi-solution
- Fr\(\acute{\text {e}}\)chet gradient
- Stability
- Conjugate gradient method