论文标题
经典解决方案对具有信号依赖性动作的识别凯勒（Keller）模型的界限
Boundedness of Classical Solutions to a Degenerate Keller--Segel Type Model with Signal-dependent Motilities
论文作者
论文摘要
在本文中，我们考虑了凯勒（Keller）的脱名式动力学模型的初始neumann边界价值问题。该系统具有信号依赖性的降低运动函数，渐近地消失，即，随着信号的浓度倾向于无穷大。在目前的工作中，当运动函数满足某些衰减率假设时，我们对经典解决方案的界限感兴趣。粗略地说，在二维设置中，我们证明，如果在高信号浓度下的运动函数降低的速度慢于指数速度，则将经典解决方案在全球范围内界定。在较高的维度中，当运动能力以某些代数速度降低时，将获得界限。证明基于我们先前的工作中开发的比较方法\ cite {fj19a，fj19b}以及修改的alikakos-moser型迭代。此外，还构建了涉及某些加权能量的新估计以建立界限。
In this paper, we consider the initial Neumann boundary value problem for a degenerate kinetic model of Keller--Segel type. The system features a signal-dependent decreasing motility function that vanishes asymptotically, i.e., degeneracies may take place as the concentration of signals tends to infinity. In the present work, we are interested in the boundedness of classical solutions when the motility function satisfies certain decay rate assumptions. Roughly speaking, in the two-dimensional setting, we prove that classical solution is globally bounded if the motility function decreases slower than an exponential speed at high signal concentrations. In higher dimensions, boundedness is obtained when the motility decreases at certain algebraical speed. The proof is based on the comparison methods developed in our previous work \cite{FJ19a,FJ19b} together with a modified Alikakos--Moser type iteration. Besides, new estimations involving certain weighted energies are also constructed to establish the boundedness.
