A non-stationary iterative Tikhonov regularization method for simultaneous inversion in a time-fractional diffusion equation

Wen, Jiqiu; Liu, Zhuan-Xia; Wang, Shanshan

doi:10.1016/j.cam.2023.115094

Cited by 9 publications

(2 citation statements)

References 41 publications

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“…For example, Zhang and Xu [64] and Li et al [30] discussed the uniqueness of the inverse source problem for the 1D time-fractional diffusion equation; Jiang et al [19] established the results parallel to [64] for the multi-dimensional case by constructing a weak type unique continuation, and proposed the iteration algorithm for the numerical treatment. For some other works about the fractional inverse problems, we refer to [6,24,31,32,38,53,55,57,60,61,63,65] and the references therein.…”

Section: Literaturementioning

confidence: 99%

Well-posedness of the stochastic time-fractional diffusion and wave equations and inverse random source problems

Lassas

Zhang

2023

Inverse Problems

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In this paper, we are concerned with the stochastic time-fractional diffusion-wave equations in a Hilbert space. The main objective of this paper is to establish properties of the stochastic weak solutions of the initial-boundary value problem, such as the existence, uniqueness and regularity estimates. Moreover, we apply the obtained theories to an inverse source problem. The uniqueness of this inverse problem under the boundary measurements is proved.

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Section: Literaturementioning

confidence: 99%

Well-posedness of the stochastic time-fractional diffusion and wave equations and inverse random source problems

Lassas

Zhang

2023

Inverse Problems

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“…However, to the best of our knowledge, there are few researches on simultaneous inversion of source term and initial value of time fractional diffusion equation. Jin [15,16] et al studied the simultaneous identification of the source term and initial value of the time fractional diffusion equation, but did not give the error estimates. Ruan [10] et al used the standard Tikhonov regularization method to simultaneously identify the source term and initial value of the time fractional diffusion equation.…”

Section: Introductionmentioning

confidence: 99%

Simultaneous Inversion of the Source Term and Initial Value of the Time Fractional Diffusion Equation

Yang,

Xu,

2024

Mathematical Modelling and Analysis

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In this paper, the problem we investigate is to simultaneously identify the source term and initial value of the time fractional diffusion equation. This problem is ill-posed, i.e., the solution (if exists) does not depend on the measurable data. We give the conditional stability result under the a-priori bound assumption for the exact solution. The modified Tikhonov regularization method is used to solve this problem, and under the a-priori and the a-posteriori selection rule for the regularization parameter, the convergence error estimations for this method are obtained. Finally, numerical example is given to prove the effectiveness of this regularization method.

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A mollifier approach to the simultaneous identification of the unknown source and initial distribution in a space-fractional diffusion equation

Qiao,

Xiong

2025

Applied Mathematics and Computation

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A non-stationary iterative Tikhonov regularization method for simultaneous inversion in a time-fractional diffusion equation

Cited by 9 publications

References 41 publications

Well-posedness of the stochastic time-fractional diffusion and wave equations and inverse random source problems

Well-posedness of the stochastic time-fractional diffusion and wave equations and inverse random source problems

Simultaneous Inversion of the Source Term and Initial Value of the Time Fractional Diffusion Equation

A mollifier approach to the simultaneous identification of the unknown source and initial distribution in a space-fractional diffusion equation

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