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.
Mots clés : 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 }, pages = {603--621}, publisher = {EDP-Sciences}, volume = {48}, number = {2}, year = {2014}, doi = {10.1051/m2an/2013107}, mrnumber = {3177859}, zbl = {1295.35378}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2013107/} }
TY - JOUR AU - Wei, Ting AU - Wang, Jun-Gang TI - A modified quasi-boundary value method for the backward time-fractional diffusion problem JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2014 SP - 603 EP - 621 VL - 48 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2013107/ DO - 10.1051/m2an/2013107 LA - en ID - M2AN_2014__48_2_603_0 ER -
%0 Journal Article %A Wei, Ting %A Wang, Jun-Gang %T A modified quasi-boundary value method for the backward time-fractional diffusion problem %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2014 %P 603-621 %V 48 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2013107/ %R 10.1051/m2an/2013107 %G en %F 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 , Tome 48 (2014) no. 2, pp. 603-621. doi : 10.1051/m2an/2013107. http://www.numdam.org/articles/10.1051/m2an/2013107/
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