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

Author

Listed:
  • 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
    Faculty of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, 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)

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.

Suggested Citation

  • Le Dinh Long & Yong Zhou & Tran Thanh Binh & Nguyen Can, 2019. "A Mollification Regularization Method for the Inverse Source Problem for a Time Fractional Diffusion Equation," Mathematics, MDPI, vol. 7(11), pages 1-19, November.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1048-:d:283261
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