Discrete fragmentation equations with time-dependent coefficients
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866916285925818368 |
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| author | Kerr, Lyndsay Lamb, Wilson Langer, Matthias |
| author_facet | Kerr, Lyndsay Lamb, Wilson Langer, Matthias |
| contents | 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 $\ell^1$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_10219 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Discrete fragmentation equations with time-dependent coefficients Kerr, Lyndsay Lamb, Wilson Langer, Matthias Functional Analysis 34G10, 47D06, 80A30, 34D05 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 $\ell^1$ 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. |
| title | Discrete fragmentation equations with time-dependent coefficients |
| topic | Functional Analysis 34G10, 47D06, 80A30, 34D05 |
| url | https://arxiv.org/abs/2212.10219 |