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Determine a Space-Dependent Source Term in a Time Fractional Diffusion-Wave Equation

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Abstract

This paper is devoted to identify a space-dependent source term in a multi-dimensional time fractional diffusion-wave equation from a part of noisy boundary data. Based on the series expression of solution for the direct problem, we improve the regularity of the weak solution for the direct problem under strong conditions. And we obtain the uniqueness of inverse space-dependent source term problem by the Titchmarsh convolution theorem and the Duhamel principle. Further, we use a non-stationary iterative Tikhonov regularization method combined with a finite dimensional approximation to find a stable source term. Numerical examples are provided to show the effectiveness of the proposed method.

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Acknowledgements

This paper was supported by the NSF of China (11371181, 11771192).

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  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730030, P.R. China

    X. B. Yan & T. Wei

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  1. X. B. Yan
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  2. T. Wei
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Correspondence to X. B. Yan.

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Yan, X.B., Wei, T. Determine a Space-Dependent Source Term in a Time Fractional Diffusion-Wave Equation. Acta Appl Math 165, 163–181 (2020). https://doi.org/10.1007/s10440-019-00248-2

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