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Li, Jing; Tong, Gongsheng; Duan, Rouzi; Qin, Shanlin

Tikhonov regularization method of an inverse space-dependent source problem for a time-space fractional diffusion equation. (English) Zbl 07907282

J. Appl. Anal. Comput. 11, No. 5, 2387-2401 (2021).
Summary: The aim of this paper is to identify a space-dependent source term in the time-space fractional diffusion equation with an initial-boundary data and an additional measurement data at the final time point. A series expression for the solution of the direct problem is used to transfer the inverse problem into the first type of Fredholm integral equation. Before solving the inverse problem, the uniqueness of its solution is proved. We then use the Tikhonov regularization method to deal with the integral equation and obtain a series expression for the regularized solution of the inverse problem. Moreover, according to the prior and the posterior regularization parameter selection rules, we prove the convergence rates of the regularization solution. Finally, we provide some numerical experiments to show the effectiveness of our method.

Cited in 1 Document

MSC:

65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs
65N20 Numerical methods for ill-posed problems for boundary value problems involving PDEs
47A52 Linear operators and ill-posed problems, regularization

Keywords:

inverse space-dependent source problem; time-space fractional diffusion equation; Tikhonov regularization

Software:

Regularization tools
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Full Text: DOI

References:

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