A modified quasi-boundary value method for the backward time-fractional diffusion problem
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 2, p. 603-621
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In this paper, we consider a backward problem for a time-fractional diffusion equation with variable coefficients in a general bounded domain. That is to determine the initial data from a noisy final data. Based on a series expression of the solution, a conditional stability for the initial data is given. Further, we propose a modified quasi-boundary value regularization method to deal with the backward problem and obtain two kinds of convergence rates by using an a priori regularization parameter choice rule and an a posteriori regularization parameter choice rule. Numerical examples in one-dimensional and two-dimensional cases are provided to show the effectiveness of the proposed methods.

DOI : https://doi.org/10.1051/m2an/2013107
Classification:  35R11,  35R30
Keywords: backward problem, fractional diffusion equation, modified quasi-boundary value method, convergence analysis, a priori parameter choice, morozov's discrepancy principle
@article{M2AN_2014__48_2_603_0,
     author = {Wei, Ting and Wang, Jun-Gang},
     title = {A modified quasi-boundary value method for the backward time-fractional diffusion problem},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {48},
     number = {2},
     year = {2014},
     pages = {603-621},
     doi = {10.1051/m2an/2013107},
     zbl = {1295.35378},
     mrnumber = {3177859},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2014__48_2_603_0}
}
Wei, Ting; Wang, Jun-Gang. A modified quasi-boundary value method for the backward time-fractional diffusion problem. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 2, pp. 603-621. doi : 10.1051/m2an/2013107. http://www.numdam.org/item/M2AN_2014__48_2_603_0/

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