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

Le Dinh Long, Yong Zhou, Tran Thanh Binh and Nguyen Can
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Le Dinh Long: Faculty of Natural Sciences, Thu Dau Mot University, Thu Dau Mot City 820000, Binh Duong Province, Vietnam
Yong Zhou: Faculty of Information Technology, Macau University of Science and Technology, Macau 999078, China
Tran Thanh Binh: Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam
Nguyen Can: Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam

Mathematics, 2019, vol. 7, issue 11, 1-19

Abstract: 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.

Keywords: time-fractional diffusion equation; inverse problem; ill-posed problem; convergence estimates (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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