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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.22147 |
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| _version_ | 1866912669948182528 |
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| author | Meng, Xiao Lam, Kei Fong |
| author_facet | Meng, Xiao Lam, Kei Fong |
| contents | We study a system of reaction-diffusion equations posed on a bounded domain composed of subdomains separated by a connected network with a metric graph structure. The reaction-diffusion dynamics with anisotropic diffusion on the graph edges are coupled to well-mixed ODE dynamics occurring at the vertices by junction conditions, and to similar PDE dynamics occurring on adjacent subdomains through Robin-like boundary conditions. The resulting PDE-ODE system can be used in epidemiological and ecological settings to study population movement in between cluster centers along road-like structures and into the surrounding continuum. We employ a semi-Galerkin approximation to establish the well-posedness of weak solutions to the PDE-ODE system, and examine further properties such as regularity, boundedness and finite-time extinction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_22147 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Well-posedness and finite-time extinction of a PDE-ODE spatial-network model with anisotropic diffusion Meng, Xiao Lam, Kei Fong Analysis of PDEs 35K40, 35K59, 35B40, 35D40 We study a system of reaction-diffusion equations posed on a bounded domain composed of subdomains separated by a connected network with a metric graph structure. The reaction-diffusion dynamics with anisotropic diffusion on the graph edges are coupled to well-mixed ODE dynamics occurring at the vertices by junction conditions, and to similar PDE dynamics occurring on adjacent subdomains through Robin-like boundary conditions. The resulting PDE-ODE system can be used in epidemiological and ecological settings to study population movement in between cluster centers along road-like structures and into the surrounding continuum. We employ a semi-Galerkin approximation to establish the well-posedness of weak solutions to the PDE-ODE system, and examine further properties such as regularity, boundedness and finite-time extinction. |
| title | Well-posedness and finite-time extinction of a PDE-ODE spatial-network model with anisotropic diffusion |
| topic | Analysis of PDEs 35K40, 35K59, 35B40, 35D40 |
| url | https://arxiv.org/abs/2510.22147 |