Recovering the Fragmentation Rate in the Growth-Fragmentation Equation
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916129486667776 |
|---|---|
| author | Gomez, Alvaro Almeida Zubelli, Jorge |
| author_facet | Gomez, Alvaro Almeida Zubelli, Jorge |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_10918 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Recovering the Fragmentation Rate in the Growth-Fragmentation Equation Gomez, Alvaro Almeida Zubelli, Jorge Numerical Analysis 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. |
| title | Recovering the Fragmentation Rate in the Growth-Fragmentation Equation |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2402.10918 |