@article{4b48dfe8ecf34452b92c297d48364f97,

title = "Recovering the fragmentation rate in the growth-fragmentation equation",

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.",

keywords = "Fourier transform on groups, growth-fragmentation equation, mathematical biology models, regularization techniques, size-structured models",

author = "{Almeida Gomez}, Alvaro and Zubelli, {Jorge P.}",

note = "Funding Information: A A G and J P Z acknowledge support from the FSU-2020-09 Grant from Khalifa University. The authors acknowledge the financial support provided by CAPES, Coordena{\c c}{\~a}o de Aperfei{\c c}oamento de Pessoal de N{\'i}vel Superior, Grant Number 88887.311757/2018-00, CNPq, Conselho Nacional de Desenvolvimento Cient{\'i}fico e Tecnol{\'o}gico, Grant Numbers 308958/2019-5 and 307873/2013-7, and FAPERJ, Funda{\c c}{\~a}o Carlos Chagas Filho de Amparo {\`a} Pesquisa do Estado do Rio de Janeiro, Grant Nos. E-26/200.899/2021 and E-26/202.927/2017. Publisher Copyright: {\textcopyright} 2022 The Author(s). Published by IOP Publishing Ltd.",

year = "2022",

month = jan,

doi = "10.1088/1361-6420/aca048",

language = "British English",

volume = "39",

journal = "Inverse Problems",

issn = "0266-5611",

publisher = "IOP Publishing Ltd.",

number = "1",

}