论文标题
具有非单调信号依赖性运动性的完全抛物线凯勒 - 塞格系统中的全球存在和统一的界限
Global Existence and Uniform Boundedness in a Fully Parabolic Keller-Segel System with Non-monotonic Signal-dependent Motility
论文作者
论文摘要
本文涉及凯勒（Keller）完全抛物线系统的全球可溶性 - 涉及非单调信号依赖性运动性的识别型。首先，我们证明了在一定的无穷大假设下具有通用积极运动函数的经典解决方案的全球存在，但是，这允许在有限区域内的运动函数任意较大。然后，只要在任何维度$ n \ geq1 $中具有严格的正上下和上限，或者在无限速度以$ n \ geq2 $的一定缓慢速率衰减时，就建立了经典解决方案的均匀界限。我们的结果消除了在最近的一些工作中{JLZ22，FJ19B，FS22}中对运动函数的至关重要的要求，因此可以同时进行化学吸引力和化学抗性效应，或者它们在申请中的共存在。我们证明的关键要素在于对\ cite {Jlz22，fj19b，lj21}中开发的比较方法的重要改进。
This paper is concerned with global solvability of a fully parabolic system of Keller--Segel-type involving non-monotonic signal-dependent motility. First, we prove global existence of classical solutions to our problem with generic positive motility function under a certain smallness assumption at infinity, which however permits the motility function to be arbitrarily large within a finite region. Then uniform-in-time boundedness of classical solutions is established whenever the motility function has strictly positive lower and upper bounds in any dimension $N\geq1$, or decays at a certain slow rate at infinity for $N\geq2$. Our results remove the crucial non-increasing requirement on the motility function in some recent work \cite{JLZ22,FJ19b,FS22} and hence allow for both chemo-attractive and chemo-repulsive effect, or their co-existence in applications. The key ingredient of our proof lies in an important improvement of the comparison method developed in \cite{JLZ22,FJ19b,LJ21}.
