A fractional attraction-repulsion chemotaxis system with generalized logistic source and nonlinear productions
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866908916851408896 |
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| author | Song, Liyan Li, Qingchun Qu, Chengyuan |
| author_facet | Song, Liyan Li, Qingchun Qu, Chengyuan |
| contents | This paper studies a fractional attraction-repulsion system with generalized logistic source and nonlinear productions: \begin{equation*} \left\{ \begin{aligned} &u_t = -(-Δ)^αu - χ_1 \nabla \cdot (u \nabla v) + χ_2 \nabla \cdot (u \nabla w) + au - bu^γ, &x \in \mathbb{R}^N, \, t > 0, \\ &0 = Δv - λ_1 v + μ_1 u^k, &x \in \mathbb{R}^N, \, t > 0, \\ &0 = Δw - λ_2 w + μ_2 u^k, &x \in \mathbb{R}^N, \, t > 0. \end{aligned} \right. \end{equation*} We first establish the global boundedness of classical solutions with nonnegative bounded and uniformly continuous initial data in two different cases: $γ\geq k + 1$ and $γ< k + 1$, respectively. Next, we show the asymptotic behavior of the global solutions for both cases $γ= k + 1$ and $γ\neq k + 1$. Finally, we obtain the spreading speed of solutions. In particular, when $γ= k + 1$, the upper bound of the spreading speed increases monotonically with $k$. If the condition of balanced attraction-repulsion intensities is further specified, the spreading speed will be equal to $\frac{a}{N + 2α}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_26148 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A fractional attraction-repulsion chemotaxis system with generalized logistic source and nonlinear productions Song, Liyan Li, Qingchun Qu, Chengyuan Analysis of PDEs This paper studies a fractional attraction-repulsion system with generalized logistic source and nonlinear productions: \begin{equation*} \left\{ \begin{aligned} &u_t = -(-Δ)^αu - χ_1 \nabla \cdot (u \nabla v) + χ_2 \nabla \cdot (u \nabla w) + au - bu^γ, &x \in \mathbb{R}^N, \, t > 0, \\ &0 = Δv - λ_1 v + μ_1 u^k, &x \in \mathbb{R}^N, \, t > 0, \\ &0 = Δw - λ_2 w + μ_2 u^k, &x \in \mathbb{R}^N, \, t > 0. \end{aligned} \right. \end{equation*} We first establish the global boundedness of classical solutions with nonnegative bounded and uniformly continuous initial data in two different cases: $γ\geq k + 1$ and $γ< k + 1$, respectively. Next, we show the asymptotic behavior of the global solutions for both cases $γ= k + 1$ and $γ\neq k + 1$. Finally, we obtain the spreading speed of solutions. In particular, when $γ= k + 1$, the upper bound of the spreading speed increases monotonically with $k$. If the condition of balanced attraction-repulsion intensities is further specified, the spreading speed will be equal to $\frac{a}{N + 2α}$. |
| title | A fractional attraction-repulsion chemotaxis system with generalized logistic source and nonlinear productions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.26148 |