Spreading dynamics of a Fisher-KPP nonlocal diffusion model with a free boundary
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| Format: | Preprint |
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2024
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| _version_ | 1866910618457473024 |
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| author | Li, Lei Wang, Mingxin |
| author_facet | Li, Lei Wang, Mingxin |
| contents | This paper concerns the spreading speed and asymptotical behaviors, which was left as an open problem in \cite{LLW22}, of a Fisher-KPP nonlocal diffusion model with a free boundary. Using a new lower solution, we get the exact finite spreading speed of free boundary that is proved to be the asymptotical spreading speed of solution component $u$. Moreover, for the algebraic decay kernels, we derive the rates of accelerated spreading and the corresponding asymptotical behaviors of solution component $u$. Especially, for the level set $E^λ(t)$ with $λ\in(0,u^*)$, we find an interesting propagation phenomenon different from the double free boundary problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16101 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spreading dynamics of a Fisher-KPP nonlocal diffusion model with a free boundary Li, Lei Wang, Mingxin Analysis of PDEs This paper concerns the spreading speed and asymptotical behaviors, which was left as an open problem in \cite{LLW22}, of a Fisher-KPP nonlocal diffusion model with a free boundary. Using a new lower solution, we get the exact finite spreading speed of free boundary that is proved to be the asymptotical spreading speed of solution component $u$. Moreover, for the algebraic decay kernels, we derive the rates of accelerated spreading and the corresponding asymptotical behaviors of solution component $u$. Especially, for the level set $E^λ(t)$ with $λ\in(0,u^*)$, we find an interesting propagation phenomenon different from the double free boundary problem. |
| title | Spreading dynamics of a Fisher-KPP nonlocal diffusion model with a free boundary |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.16101 |