Global boundedness in the higher-dimensional fully parabolic chemotaxis with weak singular sensitivity and logistic source
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866913729918009344 |
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| author | Le, Minh |
| author_facet | Le, Minh |
| contents | We consider the following chemotaxis system under homogeneous Neumann boundary conditions in a smooth, open, bounded domain $Ω\subset \mathbb{R}^n$ with $n \geq 3$: \begin{equation*}
\begin{cases}
u_t = Δu - χ\nabla \cdot \left( \frac{u}{v^k} \nabla v \right) + ru - μu^2, & \text{in } Ω\times (0,T_{\rm max}),
v_t = Δv - αv + βu, & \text{in } Ω\times (0,T_{\rm max}),
\end{cases} \end{equation*} where $k \in (0,1)$, and $χ, r, μ, α, β$ are positive parameters. In this paper, we demonstrate that for suitably smooth initial data, the problem admits a unique nonnegative classical solution that remains globally bounded in time when $μ$ is sufficiently large. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08024 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global boundedness in the higher-dimensional fully parabolic chemotaxis with weak singular sensitivity and logistic source Le, Minh Analysis of PDEs We consider the following chemotaxis system under homogeneous Neumann boundary conditions in a smooth, open, bounded domain $Ω\subset \mathbb{R}^n$ with $n \geq 3$: \begin{equation*} \begin{cases} u_t = Δu - χ\nabla \cdot \left( \frac{u}{v^k} \nabla v \right) + ru - μu^2, & \text{in } Ω\times (0,T_{\rm max}), v_t = Δv - αv + βu, & \text{in } Ω\times (0,T_{\rm max}), \end{cases} \end{equation*} where $k \in (0,1)$, and $χ, r, μ, α, β$ are positive parameters. In this paper, we demonstrate that for suitably smooth initial data, the problem admits a unique nonnegative classical solution that remains globally bounded in time when $μ$ is sufficiently large. |
| title | Global boundedness in the higher-dimensional fully parabolic chemotaxis with weak singular sensitivity and logistic source |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2503.08024 |