Determining a Time-Varying Potential in Time-Fractional Diffusion from Observation at a Single Point
<|reference_start|>Determining a Time-Varying Potential in Time-Fractional Diffusion from Observation at a Single Point: We discuss the identification of a time-dependent potential in a time-fractional diffusion model from a boundary measurement taken at a single point. Theoretically, we establish a conditional Lipschitz stability for this inverse problem. Numerically, we develop an easily implementable iterative algorithm to recover the unknown coefficient, and also derive rigorous error bounds for the discrete reconstruction. These results are attained by using the (discrete) solution theory of direct problems, and applying error estimates that are optimal with respect to problem data regularity. Numerical simulations are provided to demonstrate the theoretical results.<|reference_end|>
@article{cen2024determining,
    title={Determining a Time-Varying Potential in Time-Fractional Diffusion from
  Observation at a Single Point},
    author={Siyu Cen, Kwancheol Shin, Zhi Zhou},
    journal={arXiv preprint arXiv:2407.15094},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.15094},
    primaryClass={math.NA cs.NA}
}