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Article

A Mollification Regularization Method for the Inverse Source Problem for a Time Fractional Diffusion Equation

1
Faculty of Natural Sciences, Thu Dau Mot University, Thu Dau Mot City 820000, Binh Duong Province, Vietnam
2
Faculty of Information Technology, Macau University of Science and Technology, Macau 999078, China
3
Faculty of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China
4
Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam
5
Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(11), 1048; https://doi.org/10.3390/math7111048
Received: 7 September 2019 / Revised: 15 October 2019 / Accepted: 29 October 2019 / Published: 4 November 2019
We consider a time-fractional diffusion equation for an inverse problem to determine an unknown source term, whereby the input data is obtained at a certain time. In general, the inverse problems are ill-posed in the sense of Hadamard. Therefore, in this study, we propose a mollification regularization method to solve this problem. In the theoretical results, the error estimate between the exact and regularized solutions is given by a priori and a posteriori parameter choice rules. Besides, the proposed regularized methods have been verified by a numerical experiment. View Full-Text
Keywords: time-fractional diffusion equation; inverse problem; ill-posed problem; convergence estimates time-fractional diffusion equation; inverse problem; ill-posed problem; convergence estimates
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MDPI and ACS Style

Long, L.D.; Zhou, Y.; Thanh Binh, T.; Can, N. A Mollification Regularization Method for the Inverse Source Problem for a Time Fractional Diffusion Equation. Mathematics 2019, 7, 1048. https://doi.org/10.3390/math7111048

AMA Style

Long LD, Zhou Y, Thanh Binh T, Can N. A Mollification Regularization Method for the Inverse Source Problem for a Time Fractional Diffusion Equation. Mathematics. 2019; 7(11):1048. https://doi.org/10.3390/math7111048

Chicago/Turabian Style

Long, Le Dinh, Yong Zhou, Tran Thanh Binh, and Nguyen Can. 2019. "A Mollification Regularization Method for the Inverse Source Problem for a Time Fractional Diffusion Equation" Mathematics 7, no. 11: 1048. https://doi.org/10.3390/math7111048

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