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Li Qiao, Ruo-Hong Li, Fan Yang, Xiao-Xiao Li. SIMULTANEOUS INVERSION OF THE SOURCE TERM AND INITIAL VALUE OF THE MULTI-TERM TIME FRACTIONAL SLOW DIFFUSION EQUATION[J]. Journal of Applied Analysis & Computation, 2025, 15(4): 1903-1927. doi: 10.11948/20240328
Citation: Li Qiao, Ruo-Hong Li, Fan Yang, Xiao-Xiao Li. SIMULTANEOUS INVERSION OF THE SOURCE TERM AND INITIAL VALUE OF THE MULTI-TERM TIME FRACTIONAL SLOW DIFFUSION EQUATION[J]. Journal of Applied Analysis & Computation, 2025, 15(4): 1903-1927. doi: 10.11948/20240328
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SIMULTANEOUS INVERSION OF THE SOURCE TERM AND INITIAL VALUE OF THE MULTI-TERM TIME FRACTIONAL SLOW DIFFUSION EQUATION

  • School of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, China

    Abstract

  • In this paper, the inverse problem of simultaneously identifying the source term and initial value for the multi-term time fractional diffusion equation is studied. We prove this problem is ill-posed, i.e. the solution (if it exists) does not continuous depend on measurement data. A standard Tikhonov regularization method is proposed to solve the inverse problem. In the case of a-priori and a-posteriori, we derive the error estimates between the exact solution and the regularized solution. Finally, we provide two examples to show the validity of the proposed method.

    MSC: 35R25, 47A52, 35R30
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