Recovering the Fragmentation Rate in the Growth-Fragmentation Equation
<|reference_start|>Recovering the Fragmentation Rate in the Growth-Fragmentation Equation: We consider the inverse problem of determining the fragmentation rate from noisy measurements in the growth-fragmentation equation. We use Fourier transform theory on locally compact groups to treat this problem for general fragmentation probabilities. We develop a regularization method based on spectral filtering, which allows us to deal with the inverse problem in weighted ${L}^2$ spaces. %Our approach regularizes the signal generated by differential operators in the frequency domain. As a result, we obtain a regularization method with error of order $O(\varepsilon^{\frac{2m}{2m+1}})$, where $\varepsilon$ is the noise level and $m>0$ is the {\em a priori} regularity order of the fragmentation rate.<|reference_end|>
@article{gomez2024recovering,
    title={Recovering the Fragmentation Rate in the Growth-Fragmentation Equation},
    author={Alvaro Almeida Gomez, Jorge Zubelli},
    journal={Inverse Problems, 2022},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.10918},
    primaryClass={math.NA cs.NA}
}