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Critical mass on the Keller-Segel system with signal-dependent motility
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-07-29 , DOI: 10.1090/proc/15124 Hai-Yang Jin , Zhi-An Wang
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-07-29 , DOI: 10.1090/proc/15124 Hai-Yang Jin , Zhi-An Wang
Abstract:This paper is concerned with the global boundedness and blow-up of solutions to the Keller-Segel system with density-dependent motility in a two-dimensional bounded smooth domain with Neumman boundary conditions. We show that if the motility function decays exponentially, then a critical mass phenomenon similar to the minimal Keller-Segel model will arise. That is, there is a number 
, such that the solution will globally exist with uniform-in-time bound if the initial cell mass (i.e., 
-norm of the initial value of cell density) is less than 
, while the solution may blow up if the initial cell mass is greater than 
.
中文翻译：
Keller-Segel系统上的临界质量具有与信号有关的运动性
摘要：本文涉及具有Neumman边界条件的二维有界光滑域中具有密度依赖性运动的Keller-Segel系统解的整体有界性和爆炸性。我们表明，如果运动功能呈指数衰减，那么将出现类似于最小Keller-Segel模型的临界质量现象。也就是说，有一个数字，如果初始细胞质量（即，细胞密度初始值的-范数）小于，则溶液将以统一的时间范围全局存在，而溶液可能会爆炸如果初始细胞质量大于。
更新日期：2020-09-02
, such that the solution will globally exist with uniform-in-time bound if the initial cell mass (i.e., -norm of the initial value of cell density) is less than , while the solution may blow up if the initial cell mass is greater than . 中文翻译：
Keller-Segel系统上的临界质量具有与信号有关的运动性
摘要：本文涉及具有Neumman边界条件的二维有界光滑域中具有密度依赖性运动的Keller-Segel系统解的整体有界性和爆炸性。我们表明，如果运动功能呈指数衰减，那么将出现类似于最小Keller-Segel模型的临界质量现象。也就是说，有一个数字
，如果初始细胞质量（即，细胞密度初始值的-范数）小于，则溶液将以统一的时间范围全局存在，而溶液可能会爆炸如果初始细胞质量大于。
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