Dynamics for a diffusive epidemic model with a free boundary: sharp asymptotic profile
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866929422151450624 |
|---|---|
| author | Li, Xueping Li, Lei Wang, Mingxin |
| author_facet | Li, Xueping Li, Lei Wang, Mingxin |
| contents | This paper concerns the sharp asymptotic profiles of the solution of a diffusive epidemic model with one free boundary and one fixed boundary which is subject to the homogeneous Dirichlet boundary condition and Neumann boundary condition, respectively. The longtime behaviors has been proved to be governed by a spreading-vanishing dichotomy in \cite{LL}, and when spreading happens, the spreading speed is determined in \cite{LLW}. In this paper, by constructing some subtle upper and lower solutions, as well as employing some detailed analysis, we improve the results in \cite{LLW} and obtain the sharp asymptotic spreading profiles, which show the homogeneous Dirichlet boundary condition and Neumann boundary condition imposed at the fixed boundary $x=0$ lead to the same asymptotic behaviors of $h(t)$ and $(u,v)$ near the spreading front $h(t)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_11702 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamics for a diffusive epidemic model with a free boundary: sharp asymptotic profile Li, Xueping Li, Lei Wang, Mingxin Analysis of PDEs This paper concerns the sharp asymptotic profiles of the solution of a diffusive epidemic model with one free boundary and one fixed boundary which is subject to the homogeneous Dirichlet boundary condition and Neumann boundary condition, respectively. The longtime behaviors has been proved to be governed by a spreading-vanishing dichotomy in \cite{LL}, and when spreading happens, the spreading speed is determined in \cite{LLW}. In this paper, by constructing some subtle upper and lower solutions, as well as employing some detailed analysis, we improve the results in \cite{LLW} and obtain the sharp asymptotic spreading profiles, which show the homogeneous Dirichlet boundary condition and Neumann boundary condition imposed at the fixed boundary $x=0$ lead to the same asymptotic behaviors of $h(t)$ and $(u,v)$ near the spreading front $h(t)$. |
| title | Dynamics for a diffusive epidemic model with a free boundary: sharp asymptotic profile |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2407.11702 |