Inverse source problem with a posteriori interior measurements for space-time fractional diffusion equations

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Hauptverfasser: Yu, Kai, Li, Zhiyuan, Liu, Yikan
Format: Preprint
Veröffentlicht: 2025
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author Yu, Kai
Li, Zhiyuan
Liu, Yikan
author_facet Yu, Kai
Li, Zhiyuan
Liu, Yikan
contents This paper investigates an inverse source problem for space-time fractional diffusion equations from a posteriori interior measurements. The uniqueness result is established by the memory effect of fractional derivatives and the unique continuation property. For the numerical reconstruction, the inverse problem is reformulated as an optimization problem with the Tikhonov regularization. We use the Levenberg-Marquardt method to identity the unknown source from noisy measurements. Finally, we give some numerical examples to illustrate the efficiency and accuracy of the proposed algorithm.
format Preprint
id arxiv_https___arxiv_org_abs_2506_21070
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Inverse source problem with a posteriori interior measurements for space-time fractional diffusion equations
Yu, Kai
Li, Zhiyuan
Liu, Yikan
Numerical Analysis
35R30, 35R11
This paper investigates an inverse source problem for space-time fractional diffusion equations from a posteriori interior measurements. The uniqueness result is established by the memory effect of fractional derivatives and the unique continuation property. For the numerical reconstruction, the inverse problem is reformulated as an optimization problem with the Tikhonov regularization. We use the Levenberg-Marquardt method to identity the unknown source from noisy measurements. Finally, we give some numerical examples to illustrate the efficiency and accuracy of the proposed algorithm.
title Inverse source problem with a posteriori interior measurements for space-time fractional diffusion equations
topic Numerical Analysis
35R30, 35R11
url https://arxiv.org/abs/2506.21070