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.
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 |
|---|---|
| Pages (from-to) | 1947-1965 |
| Number of pages | 19 |
| Journal | Discrete and Continuous Dynamical Systems - series S |
| Volume | 17 |
| Issue number | 5&6 |
| Early online date | 4 Jan 2023 |
| DOIs | |
| Publication status | Published - 20 May 2024 |
Funding
2020 Mathematics Subject Classification. Primary: 34G10, 47D06; Secondary: 80A30, 34D05. Key words and phrases. Discrete fragmentation, non-autonomous evolution equation, evolution family, long-time behaviour. The first author gratefully acknowledges the support of The Carnegie Trust for the Universities of Scotland. Further, the first author is a cross-disciplinary post-doctoral fellow supported by funding from the University of Edinburgh and Medical Research Council (MC UU 00009/2). \u2217Corresponding author: Matthias Langer.
Keywords
- discrete fragmentation
- non-autonomous evolution equation
- evolution family
- long-time behaviour