In this work we describe a hyperbolic model with cell-cell repulsion with a dynamics in the population of cells. More precisely, we consider a population of cells producing a field (which we call "pressure") which induces a motion of the cells following the opposite of the gradient. The field indicates the local density of population and we assume that cells try to avoid crowded areas and prefer locally empty spaces which are far away from the carrying capacity. We analyze the well-posed property of the associated Cauchy problem on the real line. Moreover we obtain a convergence result for bounded initial distributions which are positive and stay away from zero uniformly on the real line.

中文翻译：

---

双曲Keller-Segel方程解的存在性和唯一性

在这项工作中，我们描述了具有细胞间排斥力的双曲线模型，其中细胞群具有动态变化。更精确地，我们考虑了产生场（我们称为“压力”）的细胞群，该场诱导细胞按照梯度的相反方向运动。该字段指示人口的局部密度，我们假设细胞试图避开拥挤的区域，而偏爱远离承载能力的局部空旷的空间。我们在实际线上分析了相关柯西问题的适定性质。此外，我们获得了有界初始分布的收敛结果，该有界初始分布为正并在实线上均匀地远离零。