Recovering the fragmentation rate in the growth-fragmentation equation. (1st January 2023)

• Record Type: Journal Article
• Authors: Almeida Gomez, Alvaro; Zubelli, Jorge P
• Is Part Of: Inverse problems. Volume 39:Number 1(2023)
• Publication Date: 2023-01-01
• Subjects: size-structured models -- regularization techniques -- Fourier transform on groups -- growth-fragmentation equation -- mathematical biology models; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aca048
• Languages: English
• ISSNs: 0266-5611

Abstract

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. As a result, we obtain a regularization method with error of order O ( ε 2 m 2 m + 1 ), where ɛ is the noise level and m > 0 is the a priori regularity order of the fragmentation rate.