English

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

Numerical Analysis 2025-10-24 v2 Numerical Analysis

Abstract

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.

Keywords

Cite

@article{arxiv.2506.21070,
  title  = {Inverse source problem with a posteriori interior measurements for space-time fractional diffusion equations},
  author = {Kai Yu and Zhiyuan Li and Yikan Liu},
  journal= {arXiv preprint arXiv:2506.21070},
  year   = {2025}
}

Comments

14 pages, 2 figures, 2 tables

R2 v1 2026-07-01T03:34:09.517Z