Parameter identification in PDEs by the solution of monotone inclusion problems
<|reference_start|>Parameter identification in PDEs by the solution of monotone inclusion problems: In this paper we consider a parameter identification problem for a semilinear parabolic PDE. For the regularized solution of this problem, we introduce a total variation based regularization method requiring the solution of a monotone inclusion problem. We show well-posedness in the sense of inverse problems of the resulting regularization scheme. In addition, we introduce and analyze a numerical algorithm for the solution of this inclusion problem using a nested inertial primal dual method. We demonstrate by means of numerical examples the convergence of both the numerical algorithm and the regularization method.<|reference_end|>
@article{gautam2024parameter,
    title={Parameter identification in PDEs by the solution of monotone inclusion
  problems},
    author={Pankaj Gautam and Markus Grasmair},
    journal={arXiv preprint arXiv:2403.04557},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.04557},
    primaryClass={math.NA cs.NA math.AP math.OC}
}