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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.25569 |
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Table of Contents:
- This paper studies a fractional attraction-repulsion system with time-space dependent growth source and nonlinear productions: \begin{equation*} \left\{ \begin{aligned}\label{1.1} &u_t = -(-Δ)^αu - χ_1 \nabla \cdot (u \nabla v_1) + χ_2 \nabla \cdot (u \nabla v_2) + a(x,t)u - b(x,t)u^γ, &x \in \mathbb{R}^N, \, t > 0, \\ &0 = Δv_1 - λ_1 v_1 + μ_1 u^k, &x \in \mathbb{R}^N, \, t > 0, \\ &0 = Δv_2 - λ_2 v_2 + 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. For a fixed $γ$, when $k$ exceeds the critical value $γ- 1$, a larger $b$ must be chosen to suppress the blow-up of the solution. Moreover, we show the persistence of the global solutions for both cases $γ= k + 1$ and $γ\neq k + 1$.