Analysis of a parabolic-hyperbolic hybrid population model
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915493253742592 |
|---|---|
| author | Huang, Qihua Wang, Minglong Wu, Yixiang |
| author_facet | Huang, Qihua Wang, Minglong Wu, Yixiang |
| contents | This paper is concerned with the global dynamics of a hybrid parabolic-hyperbolic model describing populations with distinct dispersal and sedentary stages. We first establish the global well-posedness of solutions, prove a comparison principle, and demonstrate the asymptotic smoothness of the solution semiflow. Through the spectral analysis of the linearized system, we derive and characterize the net reproductive rate $\mathcal{R}_{0}$. Furthermore, an explicit relationship between $\mathcal{R}_{0}$ and the principal eigenvalue of the linearized system is analyzed. Under appropriate monotonicity assumptions, we show that $\mathcal{R}_{0}$ serves as a threshold parameter that completely determines the stability of steady states of the system. More precisely, when $\mathcal{R}_{0}<1$, the trivial equilibrium is globally asymptotical stable, while when $\mathcal{R}_{0}>1$, the system is uniformly persistent and there is a positive equilibrium which is unique and globally asymptotical stable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12833 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Analysis of a parabolic-hyperbolic hybrid population model Huang, Qihua Wang, Minglong Wu, Yixiang Analysis of PDEs 92D25, 35K57, 35L50, 35B40 This paper is concerned with the global dynamics of a hybrid parabolic-hyperbolic model describing populations with distinct dispersal and sedentary stages. We first establish the global well-posedness of solutions, prove a comparison principle, and demonstrate the asymptotic smoothness of the solution semiflow. Through the spectral analysis of the linearized system, we derive and characterize the net reproductive rate $\mathcal{R}_{0}$. Furthermore, an explicit relationship between $\mathcal{R}_{0}$ and the principal eigenvalue of the linearized system is analyzed. Under appropriate monotonicity assumptions, we show that $\mathcal{R}_{0}$ serves as a threshold parameter that completely determines the stability of steady states of the system. More precisely, when $\mathcal{R}_{0}<1$, the trivial equilibrium is globally asymptotical stable, while when $\mathcal{R}_{0}>1$, the system is uniformly persistent and there is a positive equilibrium which is unique and globally asymptotical stable. |
| title | Analysis of a parabolic-hyperbolic hybrid population model |
| topic | Analysis of PDEs 92D25, 35K57, 35L50, 35B40 |
| url | https://arxiv.org/abs/2507.12833 |