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Identification of Source Term for the Time-Fractional Diffusion-Wave Equation by Fractional Tikhonov Method

Author

Listed:
  • Le Dinh Long

    (Faculty of Natural Sciences, Thu Dau Mot University, Thu Dau Mot City 820000, Binh Duong Province, Vietnam
    These authors contributed equally to this work.)

  • Nguyen Hoang Luc

    (Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam
    These authors contributed equally to this work.)

  • Yong Zhou

    (Faculty of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China
    Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    These authors contributed equally to this work.)

  • and Can Nguyen

    (Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam
    These authors contributed equally to this work.)

Abstract

In this article, we consider an inverse problem to determine an unknown source term in a space-time-fractional diffusion equation. The inverse problems are often ill-posed. By an example, we show that this problem is NOT well-posed in the Hadamard sense, i.e., this problem does not satisfy the last condition-the solution’s behavior changes continuously with the input data. It leads to having a regularization model for this problem. We use the Tikhonov method to solve the problem. In the theoretical results, we also propose a priori and a posteriori parameter choice rules and analyze them.

Suggested Citation

  • Le Dinh Long & Nguyen Hoang Luc & Yong Zhou & and Can Nguyen, 2019. "Identification of Source Term for the Time-Fractional Diffusion-Wave Equation by Fractional Tikhonov Method," Mathematics, MDPI, vol. 7(10), pages 1-24, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:934-:d:274849
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