On a backward problem for inhomogeneous time-fractional diffusion equations

In this paper, we consider a final value problem for time-fractional diffusion equation with inhomogeneous source. The main goal of our paper is to determine an approximated initial data from the observation data at final time by constructing a regularized solution using a mollification method. Unde...

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Veröffentlicht in:Computers & mathematics with applications (1987) 2019-09, Vol.78 (5), p.1317-1333
Hauptverfasser: Luc, Nguyen Hoang, Huynh, Le Nhat, Tuan, Nguyen Huy, Long, Le Dinh
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Sprache:eng
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Zusammenfassung:In this paper, we consider a final value problem for time-fractional diffusion equation with inhomogeneous source. The main goal of our paper is to determine an approximated initial data from the observation data at final time by constructing a regularized solution using a mollification method. Under appropriate regularity assumptions of the exact solution, we give convergence rate between the reconstructed solution and the exact one. We also provide a numerical example to illustrate the main results.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2019.02.014