Recovering the fragmentation rate in the growth-fragmentation equation

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.