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Volume 5, Issue 3
Tikhonov Regularisation Method for Simultaneous Inversion of the Source Term and Initial Data in a Time-Fractional Diffusion Equation

Zhousheng Ruan, Jerry Zhijian Yang & Xiliang Lu

East Asian J. Appl. Math., 5 (2015), pp. 273-300.

Published online: 2018-02

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  • Abstract

The inverse problem of identifying the time-independent source term and initial value simultaneously for a time-fractional diffusion equation is investigated. This inverse problem is reformulated into an operator equation based on the Fourier method. Under a certain smoothness assumption, conditional stability is established. A standard Tikhonov regularisation method is proposed to solve the inverse problem. Furthermore, the convergence rate is given for an a priori and a posteriori regularisation parameter choice rule, respectively. Several numerical examples, including one-dimensional and two-dimensional cases, show the efficiency of our proposed method.

  • AMS Subject Headings

65N21, 49M15

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COPYRIGHT: © Global Science Press

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@Article{EAJAM-5-273, author = {}, title = {Tikhonov Regularisation Method for Simultaneous Inversion of the Source Term and Initial Data in a Time-Fractional Diffusion Equation}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {5}, number = {3}, pages = {273--300}, abstract = {

The inverse problem of identifying the time-independent source term and initial value simultaneously for a time-fractional diffusion equation is investigated. This inverse problem is reformulated into an operator equation based on the Fourier method. Under a certain smoothness assumption, conditional stability is established. A standard Tikhonov regularisation method is proposed to solve the inverse problem. Furthermore, the convergence rate is given for an a priori and a posteriori regularisation parameter choice rule, respectively. Several numerical examples, including one-dimensional and two-dimensional cases, show the efficiency of our proposed method.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.310315.030715a}, url = {http://global-sci.org/intro/article_detail/eajam/10810.html} }
TY - JOUR T1 - Tikhonov Regularisation Method for Simultaneous Inversion of the Source Term and Initial Data in a Time-Fractional Diffusion Equation JO - East Asian Journal on Applied Mathematics VL - 3 SP - 273 EP - 300 PY - 2018 DA - 2018/02 SN - 5 DO - http://doi.org/10.4208/eajam.310315.030715a UR - https://global-sci.org/intro/article_detail/eajam/10810.html KW - Time-fractional diffusion equation, conditional stability, Tikhonov regularisation, Morozov discrepancy principle, convergence rate. AB -

The inverse problem of identifying the time-independent source term and initial value simultaneously for a time-fractional diffusion equation is investigated. This inverse problem is reformulated into an operator equation based on the Fourier method. Under a certain smoothness assumption, conditional stability is established. A standard Tikhonov regularisation method is proposed to solve the inverse problem. Furthermore, the convergence rate is given for an a priori and a posteriori regularisation parameter choice rule, respectively. Several numerical examples, including one-dimensional and two-dimensional cases, show the efficiency of our proposed method.

Zhousheng Ruan, Jerry Zhijian Yang & Xiliang Lu. (1970). Tikhonov Regularisation Method for Simultaneous Inversion of the Source Term and Initial Data in a Time-Fractional Diffusion Equation. East Asian Journal on Applied Mathematics. 5 (3). 273-300. doi:10.4208/eajam.310315.030715a
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