论文标题
在抛物线 - 纤维化凯勒（segel）模型中具有信号依赖性运动的界限和指数稳定
Boundedness and Exponential Stabilization in a Parabolic-Elliptic Keller--Segel Model with Signal-dependent Motilities for Local Sensing Chemotaxis
论文作者
论文摘要
在本文中，我们考虑了退化凯勒的初始neumann边界值问题 - segel模型具有信号依赖性的非激动运动函数。分析的主要障碍来自当信号浓度无限制时可能的退化。在当前的工作中，我们对较高维度的经典解决方案的界限和指数稳定性感兴趣。借助Lyapunov的功能和精致的Alikakos- Moser型迭代，我们能够建立浓度的时间独立的上限，前提是运动函数逐体降低。然后，我们通过构建涉及加权能量的估计来进一步证明溶液的均匀界限。最后，由于Lyapunov的功能再次，我们证明了对空间均匀稳态的指数稳定。我们的界限结果改善了\ cite {anh19，fj20a}中的结果，并首次获得指数稳定。
In this paper we consider the initial Neumann boundary value problem for a degenerate Keller--Segel model which features a signal-dependent non-increasing motility function. The main obstacle of analysis comes from the possible degeneracy when the signal concentration becomes unbounded. In the current work, we are interested in boundedness and exponential stability of the classical solution in higher dimensions. With the aid of a Lyapunov functional and a delicate Alikakos--Moser type iteration, we are able to establish a time-independent upper bound of the concentration provided that the motility function decreases algebraically. Then we further prove the uniform-in-time boundedness of the solution by constructing of an estimation involving a weighted energy. Finally, thanks to the Lyapunov functional again, we prove the exponential stabilization toward the spatially homogeneous steady states. Our boundedness result improves those in \cite{Anh19,FJ20a} and the exponential stabilization is obtained for the first time.
