Long time asymptotic behavior of a self-similar fragmentation equation

Gaetano Agazzotti (1) , Madalina Deaconu (2, 3) , Antoine Lejay (3, 2)

1 ENSMN - Ecole Nationale Supérieure des Mines de Nancy
2 IECL - Institut Élie Cartan de Lorraine
3 PASTA - Processus aléatoires spatio-temporels et leurs applications

Using the Mellin transform, we study a self-similar fragmentation equations whose breakage rate follows the power law distribution, and a particle is split into a fixed number of smaller particles. First, we show how to extend the solution of such equations to mesure-valued initial conditions, by a closure argument on the Mellin space. Second, we use appropriate series representations to give a rigorous proof to the asymptotic behavior of the moments, completing some results known through heuristic derivations.

Domaines: Mathématiques [math]

Gaetano Agazzotti, Madalina Deaconu, Antoine Lejay. Long time asymptotic behavior of a self-similar fragmentation equation. 2024. ⟨hal-04477123⟩