A mixed discrete-continuous fragmentation model

Journal article

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.

Authors: Baird, G; Suli, E

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Elsevier
• Journal: Journal of Mathematical Analysis and Applications
• Volume: 473
• Issue: 1
• Pages: 273-296
• Publication date: 2018-12-21
• Acceptance date: 2018-12-18
• DOI: 10.1016/j.jmaa.2018.12.048
• ISSN: 0022-247X
• Keywords: substochastic semigroups; fragmentation models; existence and uniqueness of solution; mixed discrete–continuous fragmentation model