Abstract
In this paper, we consider a problem of recovering a space-dependent source term for the Rayleigh–Stokes equation, where the additional data is the observation at a final moment $t = T$, which is ill-posed in the sense of Hadamard. Firstly, the uniqueness, ill-posedness and the conditional stability of inverse source problem is given. Next, we develop a filter regularization method to overcome the ill-posedness of the problem. Under reasonable a priori bound assumption about the source function, a Hölder-type error estimate of the regularized solution is proved for a priori regularization parameter choice rule. Furthermore, a logarithmic-type error estimate between the exact solution and the regularized solution is established based on a posteriori regularization parameter choice rule.
Funding Statement
This research is supported by Research Project of Higher School Science and Technology in Hebei Province (QN2021305).
Acknowledgments
The author would like to thanks the editor and the referees for their valuable comments and suggestions that improve the quality of our paper.
Citation
Songshu Liu. "Filter Regularization Method for Inverse Source Problem of the Rayleigh–Stokes Equation." Taiwanese J. Math. 27 (5) 847 - 861, October, 2023. https://doi.org/10.11650/tjm/230302
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