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Simultaneous recovery of multiple parameters in nonlocal diffusion equations from internal measurements
Abstract
This paper is devoted to simultaneously recovering multiple parameters from internal measurements for nonlocal diffusion equations. The uniqueness of the inverse problem is established by employing the asymptotic behavior of solutions, analytic continuation, the Laplace transform, and properties of analytic functions. For numerical reconstruction, we apply the Levenberg-Marquardt method to obtain a stable approximate solution of the inverse problem. Numerical examples are provided to demonstrate the efficiency of the proposed algorithm and to validate our theoretical findings.
Versions
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BibTeX
@misc{yu2026simultaneous,
title = {{Simultaneous recovery of multiple parameters in nonlocal diffusion equations from internal measurements}},
author = {Kai Yu and Zhiyuan Li and Yikan Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.08699},
eprint = {2606.08699},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.08699},
}
RIS
TY - UNPB
TI - Simultaneous recovery of multiple parameters in nonlocal diffusion equations from internal measurements
AU - Kai Yu
AU - Zhiyuan Li
AU - Yikan Liu
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2606.08699
UR - https://arxiv.org/abs/2606.08699
AB - This paper is devoted to simultaneously recovering multiple parameters from internal measurements for nonlocal diffusion equations. The uniqueness of the inverse problem is established by employing the asymptotic behavior of solutions, analytic continuation, the Laplace transform, and properties of analytic functions. For numerical reconstruction, we apply the Levenberg-Marquardt method to obtain a stable approximate solution of the inverse problem. Numerical examples are provided to demonstrate the efficiency of the proposed algorithm and to validate our theoretical findings.
ER -