Discrete fragmentation equations with time-dependent coefficients

Lyndsay Kerr; Wilson Lamb; Matthias Langer

doi:10.3934/dcdss.2022211

Discrete fragmentation equations with time-dependent coefficients

Lyndsay Kerr, Wilson Lamb, Matthias Langer

Mathematics And Statistics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Number of pages	19
Journal	Discrete and Continuous Dynamical Systems - series S
Early online date	4 Jan 2023
DOIs	https://doi.org/10.3934/dcdss.2022211
Publication status	E-pub ahead of print - 4 Jan 2023

Keywords

discrete fragmentation
non-autonomous evolution equation
evolution family
long-time behaviour

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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.",

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N2 - 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.

AB - 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.

KW - discrete fragmentation

KW - non-autonomous evolution equation

KW - evolution family

KW - long-time behaviour

UR - https://www.aimsciences.org/DCDS-S

U2 - 10.3934/dcdss.2022211

DO - 10.3934/dcdss.2022211

M3 - Article

ER -

Discrete fragmentation equations with time-dependent coefficients

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