Stability of constant equilibria in a Keller--Segel system with gradient dependent chemotactic sensitivity and sublinear signal production
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910777019990016 |
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| author | Kohatsu, Shohei |
| author_facet | Kohatsu, Shohei |
| contents | This paper deals with the homogeneous Neumann boundary-value problem for the Keller--Segel system \begin{align*}
\begin{cases}
u_t=Δu - χ\nabla \cdot (u|\nabla v|^{p-2}\nabla v),\\[]
v_t=Δv - v + u^θ
\end{cases} \end{align*} in $n$-dimensional bounded smooth domains for suitably regular nonnegative initial data, where $χ> 0$, $p \in (1, \infty)$ and $θ\in (0,1]$. Under smallness conditions on $p$ and $θ$, we prove that the spatially homogeneous equilibrium solution is stable. This generalizes the result in Kohatsu--Yokota (Le Matematiche, 2023; 78; 213--237) from the case $θ= 1$ to more general values of $θ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_04370 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability of constant equilibria in a Keller--Segel system with gradient dependent chemotactic sensitivity and sublinear signal production Kohatsu, Shohei Analysis of PDEs Primary: 35B35, Secondary: 35K55, 35Q92, 92C17 This paper deals with the homogeneous Neumann boundary-value problem for the Keller--Segel system \begin{align*} \begin{cases} u_t=Δu - χ\nabla \cdot (u|\nabla v|^{p-2}\nabla v),\\[] v_t=Δv - v + u^θ \end{cases} \end{align*} in $n$-dimensional bounded smooth domains for suitably regular nonnegative initial data, where $χ> 0$, $p \in (1, \infty)$ and $θ\in (0,1]$. Under smallness conditions on $p$ and $θ$, we prove that the spatially homogeneous equilibrium solution is stable. This generalizes the result in Kohatsu--Yokota (Le Matematiche, 2023; 78; 213--237) from the case $θ= 1$ to more general values of $θ$. |
| title | Stability of constant equilibria in a Keller--Segel system with gradient dependent chemotactic sensitivity and sublinear signal production |
| topic | Analysis of PDEs Primary: 35B35, Secondary: 35K55, 35Q92, 92C17 |
| url | https://arxiv.org/abs/2501.04370 |