Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.05860 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917917368516608 |
|---|---|
| author | Lin, Xiandong Ye, Hailong Zhao, Xiao-Qiang |
| author_facet | Lin, Xiandong Ye, Hailong Zhao, Xiao-Qiang |
| contents | We propose a class of nonlocal diffusion systems on time-varying domains, and fully characterize their asymptotic dynamics in the asymptotically fixed, time-periodic and unbounded cases. The kernel is not necessarily symmetric or compactly supported, provoking anisotropic diffusion or convective effects. Due to the nonlocal diffusion on time-varying domains in our systems, some significant challenges arise, such as the lack of regularizing effects of the semigroup generated by the nonlocal operator, as well as the time-dependent inherent coupling structure in kernel. By investigating a general nonautonomous nonlocal diffusion system in the space of bounded and measurable functions, we establish a comprehensive and unified framework to rigorously examine the threshold dynamics of the original system on asymptotically fixed and time-periodic domains. In the case of an asymptotically unbounded domain, we introduce a key auxiliary function to separate vanishing coefficients from nonlocal diffusions. This enables us to construct appropriate sub-solutions and derive the global threshold dynamics via the comparison principle. The findings may be of independent interest and the developed techniques, which do not rely on the existence of the principal eigenvalue, are expected to find further applications in the related nonlocal diffusion problems. We also conduct numerical simulations based on a practical model to illustrate our analytical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_05860 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global Dynamics of Nonlocal Diffusion Systems on Time-Varying Domains Lin, Xiandong Ye, Hailong Zhao, Xiao-Qiang Analysis of PDEs 35B40, 35K57, 37C65, 92D25 We propose a class of nonlocal diffusion systems on time-varying domains, and fully characterize their asymptotic dynamics in the asymptotically fixed, time-periodic and unbounded cases. The kernel is not necessarily symmetric or compactly supported, provoking anisotropic diffusion or convective effects. Due to the nonlocal diffusion on time-varying domains in our systems, some significant challenges arise, such as the lack of regularizing effects of the semigroup generated by the nonlocal operator, as well as the time-dependent inherent coupling structure in kernel. By investigating a general nonautonomous nonlocal diffusion system in the space of bounded and measurable functions, we establish a comprehensive and unified framework to rigorously examine the threshold dynamics of the original system on asymptotically fixed and time-periodic domains. In the case of an asymptotically unbounded domain, we introduce a key auxiliary function to separate vanishing coefficients from nonlocal diffusions. This enables us to construct appropriate sub-solutions and derive the global threshold dynamics via the comparison principle. The findings may be of independent interest and the developed techniques, which do not rely on the existence of the principal eigenvalue, are expected to find further applications in the related nonlocal diffusion problems. We also conduct numerical simulations based on a practical model to illustrate our analytical results. |
| title | Global Dynamics of Nonlocal Diffusion Systems on Time-Varying Domains |
| topic | Analysis of PDEs 35B40, 35K57, 37C65, 92D25 |
| url | https://arxiv.org/abs/2502.05860 |