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)

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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 ORCID logoORCID: https://orcid.org/0000-0001-8084-6054 and Langer, Matthias ORCID logoORCID: https://orcid.org/0000-0001-8813-7914;
  • Item type:Article
    ID code:83617
    Dates:
    Date
    Event
    4 January 2023
    Published
    4 January 2023
    Published Online
    17 December 2022
    Accepted
    Keywords: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
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