A mixed discrete-continuous fragmentation model

Author: 

Baird, G
Suli, E

Publication Date: 

21 December 2018

Journal: 

Journal of Mathematical Analysis and Applications

Last Updated: 

2020-06-28T23:19:12.963+01:00

Issue: 

1

Volume: 

473

DOI: 

10.1016/j.jmaa.2018.12.048

page: 

273-296

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.

Symplectic id: 

953241

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article