no. 2
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.

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 : 10.1051/m2an/2013107
Classification : 35R11, 35R30
Mots clés : backward problem, fractional diffusion equation, modified quasi-boundary value method, convergence analysis, a priori parameter choice, morozov's discrepancy principle 
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     title = {A modified quasi-boundary value method for the backward time-fractional diffusion problem},
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     pages = {603--621},
     publisher = {EDP-Sciences},
     volume = {48},
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     year = {2014},
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     mrnumber = {3177859},
     zbl = {1295.35378},
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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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