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arXiv · 2402.10918

Recovering the Fragmentation Rate in the Growth-Fragmentation Equation

Alvaro Almeida Gomez·Jorge Zubelli
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Abstract

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.

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Alvaro Almeida Gomez, Jorge Zubelli. 2024-01-20. Recovering the Fragmentation Rate in the Growth-Fragmentation Equation. https://arxiv.org/abs/2402.10918

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