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Recovering the temperature distribution for multi-term time-fractional sideways diffusion equations

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Abstract

In the current paper, an inverse boundary value problem so-called the sideways problem for the multi-term time-fractional diffusion equation is investigated. The problem of interest includes the recovering of the diffusion distribution from the boundary data. We prove that the problem is ill-posed as the solution does not continuously depend on the boundary data. We further propose a fractional filter method to regularize the problem. The stability and convergence of the proposed method are gingerly analyzed. Two numerical examples, with the support from the fast Fourier transform (FFT), are implemented to illustrate the theoretical results. The numerical results are consistent with the theoretical analysis.

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Acknowledgements

The author is very grateful to the anonymous referees for the very careful reading and helpful suggestions which led to the improvement of the original manuscript. Tran Thi Khieu was funded by the Postdoctoral Scholarship Programme of Vingroup Innovation Foundation (VINIF), code VINIF.2023.STS.48.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, University of Science, Ho Chi Minh City, Vietnam

    Tran Thi Khieu

  2. Vietnam National University, Ho Chi Minh City, Vietnam

    Tran Thi Khieu

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  1. Tran Thi Khieu
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Correspondence to Tran Thi Khieu.

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Communicated by Vasily E. Tarasov.

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Khieu, T.T. Recovering the temperature distribution for multi-term time-fractional sideways diffusion equations. Comp. Appl. Math. 43, 233 (2024). https://doi.org/10.1007/s40314-023-02546-w

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  • DOI: https://doi.org/10.1007/s40314-023-02546-w

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