Longtime behaviors of a reducible cooperative system with nonlocal diffusions and free boundaries
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913632517881856 |
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| author | Li, Lei Wang, Mingxin |
| author_facet | Li, Lei Wang, Mingxin |
| contents | This paper aims at understanding the longtime behaviors of a reducible cooperative system with nonlocal diffusions and different free boundaries, describing the interactions of two mutually beneficial species. Compared with the irreducible and monostable cooperative system, the system we care about here has many nonnegative steady states, leading to much different and rich longtime behaviors. Moreover, since the possible nonnegative steady states on half space are non-constant, we need to employ more detailed analysis to understand the corresponding steady state problems which in turn helps us to derive a complete classification for the longtime behaviors of our problem. The spreading speeds of free boundaries and more accurate limits of $(u,v)$ as $t\to\infty$ are also discussed, and accelerated spreading can happen if some threshold conditions are violated by kernel functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_00807 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Longtime behaviors of a reducible cooperative system with nonlocal diffusions and free boundaries Li, Lei Wang, Mingxin Analysis of PDEs This paper aims at understanding the longtime behaviors of a reducible cooperative system with nonlocal diffusions and different free boundaries, describing the interactions of two mutually beneficial species. Compared with the irreducible and monostable cooperative system, the system we care about here has many nonnegative steady states, leading to much different and rich longtime behaviors. Moreover, since the possible nonnegative steady states on half space are non-constant, we need to employ more detailed analysis to understand the corresponding steady state problems which in turn helps us to derive a complete classification for the longtime behaviors of our problem. The spreading speeds of free boundaries and more accurate limits of $(u,v)$ as $t\to\infty$ are also discussed, and accelerated spreading can happen if some threshold conditions are violated by kernel functions. |
| title | Longtime behaviors of a reducible cooperative system with nonlocal diffusions and free boundaries |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2501.00807 |