A Mixed Discrete-Continuous Fragmentation Model
Abstract
Motivated by the occurrence of "shattering" mass-loss observed in purely continuous fragmentation models, this work concerns the development and the mathematical analysis of a new class of hybrid discrete--continuous fragmentation models. Once established, the model, which takes the form of an integro-differential equation coupled with a system of ordinary differential equations, is subjected to a rigorous mathematical analysis, using the theory and methods of operator semigroups and their generators. Most notably, by applying the theory relating to the Kato--Voigt perturbation theorem, honest substochastic semigroups and operator matrices, the existence of a unique, differentiable solution to the model is established. This solution is also shown to preserve nonnegativity and conserve mass.
Cite
@article{arxiv.1804.04017,
title = {A Mixed Discrete-Continuous Fragmentation Model},
author = {Graham Baird and Endre Süli},
journal= {arXiv preprint arXiv:1804.04017},
year = {2018}
}