We consider a Keller–Segel model that describes the cellular chemotactic movement away from repulsive chemical subject to logarithmic sensitivity function over a confined region in ${{\mathbb{R}}^n},\,n \le 2$ . This sensitivity function describes the empirically tested Weber–Fecher’s law of living organism’s perception of a physical stimulus. We prove that, regardless of chemotaxis strength and initial data, this repulsive system is globally well-posed and the constant solution is the global and exponential in time attractor. Our results confirm the ‘folklore’ that chemorepulsion inhibits the formation of non-trivial steady states within the logarithmic chemotaxis model, hence preventing cellular aggregation therein.

中文翻译：

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具有对数灵敏度的排斥 Keller-Segel 模型的全局和指数吸引子

我们考虑一个 Keller-Segel 模型，该模型描述了细胞趋化运动远离排斥性化学物质，在有限区域内服从对数敏感性函数。${{\mathbb{R}}^n},\,n \le 2$. 该灵敏度函数描述了经过经验测试的韦伯-费歇尔定律，即生物体对物理刺激的感知。我们证明，不管趋化强度和初始数据如何，这个排斥系统是全局适定的，常数解是全局和指数时间吸引子。我们的结果证实了“民间传说”，即化学排斥抑制对数趋化模型内非平凡稳态的形成，从而防止其中的细胞聚集。