具非线性源快扩散方程组解的熄灭

吉林大学学报(理学版)

具非线性源快扩散方程组解的熄灭

刘令¹, 王国铭², 朱立勋¹

1. 吉林建筑大学基础科学部, 长春 130118; 2. 吉林大学数学学院, 长春 130012

收稿日期:2013-03-13 出版日期:2013-09-26 发布日期:2013-09-17
通讯作者: 王国铭 E-mail:wanggm@jlu.edu.cn

Extinction of Solutions to a Fast Diffusion Systemwith Nonlinear Sources

LIU Ling¹, WANG Guoming², ZHU Lixun^1

1. Department of Basic Science, Jilin Jianzhu University, Changchun 130118, China;2. College of Mathematics, Jilin University, Changchun 130012, China

Received:2013-03-13 Online:2013-09-26 Published:2013-09-17
Contact: WANG Guoming E-mail:wanggm@jlu.edu.cn

摘要/Abstract

摘要：

考虑一类具非线性源的快扩散方程组解的熄灭性质, 先建立该问题弱解的局部存在性和一定条件下弱解的唯一性, 然后借助常微分方程组不变区域理论、积分估计和Sobolev嵌入定理, 给出了该问题解在有限时刻熄灭的充分条件. 结果表明, 当源项较弱时, 该问题可能存在在有限时刻熄灭的非负解.

关键词: 快扩散方程组, 非线性源, 熄灭

Abstract:

Aiming at the extinction properties of solutions to a fast diffusion system with nonlinear sources, the authors first established the local existence of weak solutions to this problem as well as the uniqueness under certain conditions, and then gave some sufficient conditions for the solutions to vanish in finite time with the help of the theories of invariant regions for ODES, integral estimates and Sobolev embedding theorems. The results show that the solutions may vanish in finite time when the source terms are suitably weak.

Key words: fast diffusion system, nonlinear source, extinction

中图分类号:

O175.8

刘令, 王国铭, 朱立勋. 具非线性源快扩散方程组解的熄灭[J]. 吉林大学学报(理学版), 2013, 51(05): 836-842.

LIU Ling, WANG Guoming, ZHU Lixun. Extinction of Solutions to a Fast Diffusion Systemwith Nonlinear Sources[J]. Journal of Jilin University Science Edition, 2013, 51(05): 836-842.

[1]	孙爱慧, 曹春玲. 具非线性阻尼项和源函数项双曲方程解爆破时间的下界估计[J]. 吉林大学学报(理学版), 2014, 52(06): 1227-1229.
[2]	孟繁慧, 高文杰. 一类具局部化源的快扩散方程解的熄灭[J]. 吉林大学学报(理学版), 2013, 51(06): 1041-4045.
[3]	吴秀兰, 高文杰. 具有非线性吸收项的快扩散渗流方程解的熄灭[J]. J4, 2013, 51(02): 159-163.
[4]	李春光, 秦莹, 廉松哲, 袁洪君. 具有L¹初值的非牛顿多方渗流方程解的正性和熄灭性[J]. J4, 2009, 47(01): 1-4.