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Inverse Problem to Determine Two Time-Dependent Source Factors of Fractional Diffusion-Wave Equations from Final Data and Simultaneous Reconstruction of Location and Time History of a Point Source

Author

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  • Jaan Janno

    (Department of Cybernetics, Tallinn University of Technology, Ehitajate tee 5, 19086 Tallinn, Estonia)

Abstract

In this paper, two inverse problems for the fractional diffusion-wave equation that use final data are considered. The first problem consists in the determination of two time-dependent source terms. Uniqueness for this inverse problem is established under an assumption that given space-dependent factors of these terms are “sufficiently different”. The proof uses asymptotical properties of Mittag–Leffler functions. In the second problem, the aim is to reconstruct a location and time history of a point source. The uniqueness for this problem is deduced from the uniqueness theorem for the previous problem in the one-dimensional case.

Suggested Citation

  • Jaan Janno, 2023. "Inverse Problem to Determine Two Time-Dependent Source Factors of Fractional Diffusion-Wave Equations from Final Data and Simultaneous Reconstruction of Location and Time History of a Point Source," Mathematics, MDPI, vol. 11(2), pages 1-17, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:456-:d:1036298
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    References listed on IDEAS

    as
    1. Jaan Janno, 2021. "Inverse Problems with Unknown Boundary Conditions and Final Overdetermination for Time Fractional Diffusion-Wave Equations in Cylindrical Domains," Mathematics, MDPI, vol. 9(20), pages 1-22, October.
    2. Chunlong Sun & Qian Liu & Gongsheng Li, 2017. "Conditional Well-Posedness for an Inverse Source Problem in the Diffusion Equation Using the Variational Adjoint Method," Advances in Mathematical Physics, Hindawi, vol. 2017, pages 1-6, June.
    3. Emilia Blåsten & Lassi Päivärinta & Sadia Sadique, 2020. "Unique Determination of the Shape of a Scattering Screen from a Passive Measurement," Mathematics, MDPI, vol. 8(7), pages 1-15, July.
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