Regularization of the Final Value Problem for the Time-Fractional Diffusion Equation

Mohammad F. Al-Jamal; Kamal Barghout; Nidal Abu-Libdeh

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Regularization of the Final Value Problem for the Time-Fractional Diffusion Equation

机译：Regularization of the Final Value Problem for the Time-Fractional Diffusion Equation

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摘要

We consider the backward problem of reconstructing the initial condition of a nonhomogeneous time-fractional diffusion equation from final measurements. The proposed method relies on the eigenfunction expansion of the forward solution and the Tikhonov regularization to control the instability of the underlying inverse problem. We establish stability results and we provide convergence rates under a priori and a posteriori parameter choice rules. The resulting algorithm is robust and computationally inexpensive. Two examples are included to illustrate the effectiveness and accuracy of the proposed method.

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来源
《Iranian Journal of Science》 |2023年第3期|931-941|共11页
作者
Mohammad F. Al-Jamal; Kamal Barghout; Nidal Abu-Libdeh;
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作者单位

Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, Al Khobar 31952, Saudi Arabia, Department of Mathematics, Yarmouk University, Irbid 21163, Jordan;

Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, Al Khobar 31952, Saudi Arabia;

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正文语种英语
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Inverse problems; Tikhonov regularization; Nonhomogeneous; Fractional diffusion; Backward problem; Noisy final data;

Regularization of the Final Value Problem for the Time-Fractional Diffusion Equation

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