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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2606.01219 |
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| _version_ | 1866917552373891072 |
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| author | Banasiak, Jacek Błoch, Adam |
| author_facet | Banasiak, Jacek Błoch, Adam |
| contents | In this paper, we consider a network transport model in which agents moving along the edges can contribute to dynamics at nodes or bypass them. The model takes the form of a system of first-order partial differential equations coupled with a system of ordinary differential equations, and can describe a range of phenomena, from diseases in metapopulations to migratory systems with delays, to cell differentiation processes, providing a unified platform that includes network transport and delay systems as particular cases. We prove the well-posedness of the model in $ L^p$ spaces, $ 1\leq p<\infty$, study long-term asymptotics, and illustrate the theory using an SIS disease in a metapopulation consisting of several sites where the disease develops, connected by routes along which the population can migrate, as an example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_01219 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Network transport with nonlinear dynamics at the nodes Banasiak, Jacek Błoch, Adam Analysis of PDEs Dynamical Systems 35R02, 34C12, 35B40, 35F46, 35L50, 34G20, 05C50 In this paper, we consider a network transport model in which agents moving along the edges can contribute to dynamics at nodes or bypass them. The model takes the form of a system of first-order partial differential equations coupled with a system of ordinary differential equations, and can describe a range of phenomena, from diseases in metapopulations to migratory systems with delays, to cell differentiation processes, providing a unified platform that includes network transport and delay systems as particular cases. We prove the well-posedness of the model in $ L^p$ spaces, $ 1\leq p<\infty$, study long-term asymptotics, and illustrate the theory using an SIS disease in a metapopulation consisting of several sites where the disease develops, connected by routes along which the population can migrate, as an example. |
| title | Network transport with nonlinear dynamics at the nodes |
| topic | Analysis of PDEs Dynamical Systems 35R02, 34C12, 35B40, 35F46, 35L50, 34G20, 05C50 |
| url | https://arxiv.org/abs/2606.01219 |