A mixed discrete-continuous fragmentation model

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:473

Article

Baird, Graham¹  Suli, Endre¹ 

[1] Univ Oxford, Math Inst, Oxford OX2 6GG, England

关键词: Fragmentation models;    Mixed discrete-continuous fragmentation model;    Substochastic semigroups;    Existence and uniqueness of solution;   

DOI  :  10.1016/j.jmaa.2018.12.048

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free