A modified quasi-boundary value method for the backward time-fractional diffusion problem

Ting Wei; Jun-Gang Wang

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2014)

  • Volume: 48, Issue: 2, page 603-621
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Wei, Ting, and 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 48.2 (2014): 603-621. <http://eudml.org/doc/273247>.

@article{Wei2014,
abstract = {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.},
author = {Wei, Ting, Wang, Jun-Gang},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {backward problem; fractional diffusion equation; modified quasi-boundary value method; convergence analysis; a priori parameter choice; morozov’s discrepancy principle; time-fractional diffusion equation; Morozov's discrepancy principle},
language = {eng},
number = {2},
pages = {603-621},
publisher = {EDP-Sciences},
title = {A modified quasi-boundary value method for the backward time-fractional diffusion problem},
url = {http://eudml.org/doc/273247},
volume = {48},
year = {2014},
}

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 - Modélisation Mathématique et Analyse Numérique
PY - 2014
PB - EDP-Sciences
VL - 48
IS - 2
SP - 603
EP - 621
AB - 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.
LA - eng
KW - backward problem; fractional diffusion equation; modified quasi-boundary value method; convergence analysis; a priori parameter choice; morozov’s discrepancy principle; time-fractional diffusion equation; Morozov's discrepancy principle
UR - http://eudml.org/doc/273247
ER -

References

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