Competing effects of attraction vs. repulsion in chemotaxis
Competing effects of attraction vs. repulsion in chemotaxis
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DOI：
10.1142/s0218202512500443
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发表时间：
2013
影响因子：
3.5
通讯作者：
Youshan Tao;Zhian Wang
中科院分区：
文献类型：
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作者：
Youshan Tao;Zhian Wang
考虑有界区域Ω <$n中齐次Neumann边界条件下的吸引-排斥趋化系统，其中χ ≥ 0，α > 0，β > 0，γ > 0，δ > 0，τ = 0，1.我们研究了该系统的整体可解性、有界性、爆破性、非平凡定态解的存在性以及在各种参数取值范围内的渐近行为。特别地，我们证明了当τ = 0时，如果排斥大于吸引，且满足<$γ - χα > 0，则系统在高维空间是整体适定的;当τ = 1时，如果排斥大于吸引，且满足<$γ - χα > 0，且满足β = δ，则系统在二维空间是整体适定的.因此，我们的研究结果证实了吸引-排斥是一个合理的机制，以正则化经典的Keller-Segel模型，其解决方案可能会在高维爆破。
We consider the attraction–repulsion chemotaxis system under homogeneous Neumann boundary conditions in a bounded domain Ω ⊂ ℝn with smooth boundary, where χ ≥ 0, ξ ≥ 0, α > 0, β > 0, γ > 0, δ > 0 and τ = 0, 1. We study the global solvability, boundedness, blow-up, existence of non-trivial stationary solutions and asymptotic behavior of the system for various ranges of parameter values. Particularly, we prove that the system with τ = 0 is globally well-posed in high dimensions if repulsion prevails over attraction in the sense that ξγ - χα > 0, and that the system with τ = 1 is globally well-posed in two dimensions if repulsion dominates over attraction in the sense that ξγ - χα > 0 and β = δ. Hence our results confirm that the attraction–repulsion is a plausible mechanism to regularize the classical Keller–Segel model whose solution may blow up in higher dimensions.