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Volume 9, Issue 2
The Identification of the Time-Dependent Source Term in Time-Fractional Diffusion-Wave Equations

Kai Fang Liao, Yu Shan Li & Ting Wei

DOI: 10.4208/eajam.250518.170119

East Asian J. Appl. Math., 9 (2019), pp. 330-354.

Published online: 2019-03

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  • Abstract

An inverse time-dependent source problem for a multi-dimensional fractional diffusion wave equation is considered. The regularity of the weak solution for the direct problem under strong conditions is studied and the unique solvability of the inverse problem is proved. The regularised variational problem is solved by the conjugate gradient method combined with Morozov's discrepancy principle. Numerical examples show the stability and efficiency of the method.

  • Keywords

Inverse source problem, fractional diffusion-wave equation, conjugate gradient method.

  • AMS Subject Headings

65M32, 35R11

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-9-330, author = {Kai Fang Liao, Yu Shan Li and Ting Wei}, title = {The Identification of the Time-Dependent Source Term in Time-Fractional Diffusion-Wave Equations}, journal = {East Asian Journal on Applied Mathematics}, year = {2019}, volume = {9}, number = {2}, pages = {330--354}, abstract = {

An inverse time-dependent source problem for a multi-dimensional fractional diffusion wave equation is considered. The regularity of the weak solution for the direct problem under strong conditions is studied and the unique solvability of the inverse problem is proved. The regularised variational problem is solved by the conjugate gradient method combined with Morozov's discrepancy principle. Numerical examples show the stability and efficiency of the method.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.250518.170119}, url = {http://global-sci.org/intro/article_detail/eajam/13086.html} }
TY - JOUR T1 - The Identification of the Time-Dependent Source Term in Time-Fractional Diffusion-Wave Equations AU - Kai Fang Liao, Yu Shan Li & Ting Wei JO - East Asian Journal on Applied Mathematics VL - 2 SP - 330 EP - 354 PY - 2019 DA - 2019/03 SN - 9 DO - http://doi.org/10.4208/eajam.250518.170119 UR - https://global-sci.org/intro/article_detail/eajam/13086.html KW - Inverse source problem, fractional diffusion-wave equation, conjugate gradient method. AB -

An inverse time-dependent source problem for a multi-dimensional fractional diffusion wave equation is considered. The regularity of the weak solution for the direct problem under strong conditions is studied and the unique solvability of the inverse problem is proved. The regularised variational problem is solved by the conjugate gradient method combined with Morozov's discrepancy principle. Numerical examples show the stability and efficiency of the method.

Kai Fang Liao, Yu Shan Li and Ting Wei. (2019). The Identification of the Time-Dependent Source Term in Time-Fractional Diffusion-Wave Equations. East Asian Journal on Applied Mathematics. 9 (2). 330-354. doi:10.4208/eajam.250518.170119
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