Global boundedness and asymptotic stability of the Keller-Segel system with logistic-type source in the whole space
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909345440071680 |
|---|---|
| author | Li, Qingchun Chen, Haomeng |
| author_facet | Li, Qingchun Chen, Haomeng |
| contents | In this paper, we investigate the Cauchy problem of the parabolic-parabolic Keller-Segel system with the logistic-type term $au-bu^γ$ on $\mathbb{R}^N, N\geq2$. We discuss the global boundedness of classical solutions with nonnegative bounded and uniformly continuous initial functions when $γ>1$. Moreover, based on the persistence of classical solution we show the large time behavior of the positive constant equilibria with strictly positive initial function in the case of $γ\in(1,2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08648 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global boundedness and asymptotic stability of the Keller-Segel system with logistic-type source in the whole space Li, Qingchun Chen, Haomeng Analysis of PDEs In this paper, we investigate the Cauchy problem of the parabolic-parabolic Keller-Segel system with the logistic-type term $au-bu^γ$ on $\mathbb{R}^N, N\geq2$. We discuss the global boundedness of classical solutions with nonnegative bounded and uniformly continuous initial functions when $γ>1$. Moreover, based on the persistence of classical solution we show the large time behavior of the positive constant equilibria with strictly positive initial function in the case of $γ\in(1,2)$. |
| title | Global boundedness and asymptotic stability of the Keller-Segel system with logistic-type source in the whole space |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2410.08648 |