We consider the fragmentation equation
and address the question of estimating the fragmentation parameters – i.e. the division rate and the fragmentation kernel – from measurements of the size distribution at various times. This is a natural question for any application where the sizes of the particles are measured experimentally whereas the fragmentation rates are unknown, see for instance Xue and Radford (2013)  for amyloid fibril breakage. Under the assumption of a polynomial division rate and a self-similar fragmentation kernel , we use the asymptotic behavior proved in Escobedo et al. (2004)  to obtain uniqueness of the triplet and a representation formula for . To invert this formula, one of the delicate points is to prove that the Mellin transform of the asymptotic profile never vanishes, what we do through the use of the Cauchy integral.
Cite this article
Marie Doumic, Miguel Escobedo, Magali Tournus, Estimating the division rate and kernel in the fragmentation equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 35 (2018), no. 7, pp. 1847–1884DOI 10.1016/J.ANIHPC.2018.03.004