Keller-Segel生物学方程组周期解的爆破  

Blow up of Periodic Solutions for a Class of Keller-Segel Equations Arising in Biology

作　　者：段双双[1] 黄守军[1] Duan Shuangshuang Huang Shoujun(School of Mathematics and Computer Science, Anhui Normal University, Anhui Wuhu 241002)

机构地区：[1]安徽师范大学数学计算机科学学院,安徽芜湖241002

出　　处：《数学物理学报（A辑）》2017年第2期326-341,共16页Acta Mathematica Scientia

基　　金：国家自然科学基金(11301006);安徽省自然科学基金(1408085MA01)~~

摘　　要：该文主要研究一类Keller-Segel生物学方程组柯西问题的周期解的爆破.假设初值是周期的,且初值在一个周期上的全变差满足有界性条件,可以证明Keller-Segel方程组的光滑周期解将在有限时间内爆破,同时能给出生命区间的上下界估计.In this paper, we consider the blow up phenomenon of periodic solutions to the Cauchy problem for a class of Keller-Segel equations arising in biology. The initial data is assumed to be periodic and has a bounded total variations on a periodic interval. Then we are able to prove that the smooth periodic solutions of the Keller-Segel equations will blow up in finite time. Moreover, the lifespan for the solutions is also given.

关 键 词：Keller-Segel模型 趋化性 周期解 爆破 生命区间 

分 类 号：O175.2[理学—数学]