Keller-Segel生物学方程组周期解的爆破

数学物理学报 ›› 2017, Vol. 37 ›› Issue (2): 326-341.

Keller-Segel生物学方程组周期解的爆破

段双双, 黄守军

安徽师范大学数学计算机科学学院安徽芜湖 241002

收稿日期:2016-07-12 修回日期:2016-12-23 出版日期:2017-04-26 发布日期:2017-04-26
通讯作者: 段双双 E-mail:duanss0517@126.com
作者简介:黄守军,sjhuang@mail.ahnu.edu.cn
基金资助:
国家自然科学基金（11301006）和安徽省自然科学基金（1408085MA01）

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

Duan Shuangshuang, Huang Shoujun

School of Mathematics and Computer Science, Anhui Normal University, Anhui Wuhu 241002

Received:2016-07-12 Revised:2016-12-23 Online:2017-04-26 Published:2017-04-26
Supported by:
Supported by the NSFC (11301006) and the Natural Science Foundation of Anhui Province (1408085MA01)

摘要/Abstract

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.

关键词: Keller-Segel模型, 趋化性, 周期解, 爆破, 生命区间

Abstract: 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.

Key words: Keller-Segel model, Chemotaxis, Periodic solution, Blow up, Lifespan

中图分类号:

O175.2

段双双, 黄守军. Keller-Segel生物学方程组周期解的爆破[J]. 数学物理学报, 2017, 37(2): 326-341.

Duan Shuangshuang, Huang Shoujun. Blow up of Periodic Solutions for a Class of Keller-Segel Equations Arising in Biology[J]. Acta mathematica scientia,Series A, 2017, 37(2): 326-341.

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