Reconstructing the right-hand side of a fractional subdiffusion equation from the final data

In this study, we study an inverse source problem for the time-fractional diffusion equation, where the final data t = T are given. We show that our problem is ill-posed in the sense of Hadamard. Applying a truncation method, we give the regularized solution. Finally, convergence estimates under a p...

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Veröffentlicht in:Journal of inequalities and applications 2020-02, Vol.2020 (1), p.1-15, Article 53
Hauptverfasser: Luc, Nguyen Hoang, Baleanu, Dumitru, Long, Le Dinh, Can, Nguyen-Huu
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Sprache:eng
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Zusammenfassung:In this study, we study an inverse source problem for the time-fractional diffusion equation, where the final data t = T are given. We show that our problem is ill-posed in the sense of Hadamard. Applying a truncation method, we give the regularized solution. Finally, convergence estimates under a priori and a posteriori parameter choice rules are proved.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-020-02319-7