A Mixed Discrete-Continuous Fragmentation Model

Author: 

Baird, G
Süli, E

Publication Date: 

1 May 2019

Journal: 

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Last Updated: 

2020-06-21T00:29:52.7+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: 

866464

Submitted to ORA: 

Submitted

Publication Type: 

14