A posteriori regularization parameter choice rule for a modified kernel method for a time-fractional inverse diffusion problem

Liu, Songshu; Feng, Lixin

doi:10.1016/j.cam.2018.12.038

Cited by 14 publications

(2 citation statements)

References 28 publications

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“…coefficient information, source term information might not be given and then we need to recover them by extra measured information which is able to yield some fractional diffusion inverse problems [12][13][14][15][16][17][18][19][20]. In recent years, inverse problems for fractional diffusion equation have become very active in various fields of sciences and engineering, such as biology [21,22], physics [23,24], chemistry [25], and hydrology [26].…”

Section: Introductionmentioning

confidence: 99%

An Inverse Source Problem of Space-Fractional Diffusion Equation

Liu

Feng

Zhang

2021

Bull. Malays. Math. Sci. Soc.

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This paper is devoted to an inverse space-dependent source problem for spacefractional diffusion equation. Furthermore, we show that this problem is ill-posed in the sense of Hadamard, i.e., the solution (if it exists) does not depend continuously on the data. In addition, we propose a simplified generalized Tikhonov regularization method and prove the corresponding convergence estimates by using a priori regularization parameter choice rule and a posteriori parameter choice rule, respectively. Finally, numerical examples are carried to support the theoretical results and illustrate the effectiveness of the proposed method.

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Section: Introductionmentioning

confidence: 99%

An Inverse Source Problem of Space-Fractional Diffusion Equation

Liu

Feng

Zhang

2021

Bull. Malays. Math. Sci. Soc.

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“…As long as the modified 'kernel' function satisfies som certain properties, a new regularization method can be established. In addition, the modified 'kernel' idea has been used to deal with several ill-posed problems [33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%