Discrete fragmentation equations with time-dependent coefficients
Kerr, Lyndsay and Lamb, Wilson and Langer, Matthias (2023) Discrete fragmentation equations with time-dependent coefficients. Discrete and Continuous Dynamical Systems - series S. ISSN 1937-1632 (https://doi.org/10.3934/dcdss.2022211)
![]() |
Text.
Filename: Kerr_Lamb_Langer_DCDS_2022_Discrete_fragmentation_equations_with_time_dependent.pdf
Accepted Author Manuscript Restricted to Repository staff only until 17 December 2023. License: Strathprints license 1.0 Download (661kB) | Request a copy |
Abstract
We examine an infinite, linear system of ordinary differential equations that models the evolution of fragmenting clusters, where each cluster is assumed to be composed of identical units. In contrast to previous investigations into such discrete-size fragmentation models, we allow the fragmentation coefficients to vary with time. By formulating the initial-value problem for the system as a non-autonomous abstract Cauchy problem, posed in an appropriately weighted ℓ1 space, and then applying results from the theory of evolution families, we prove the existence and uniqueness of physically relevant, classical solutions for suitably constrained coefficients.
ORCID iDs
Kerr, Lyndsay, Lamb, Wilson

-
-
Item type: Article ID code: 83617 Dates: DateEvent4 January 2023Published4 January 2023Published Online17 December 2022AcceptedKeywords: discrete fragmentation, non-autonomous evolution equation, evolution family, long-time behaviour, Mathematics, Analysis Subjects: Science > Mathematics Department: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 21 Dec 2022 16:30 Last modified: 18 Jan 2023 11:45 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/83617