[1]张 强,李俐玫.对流Cahn-Hilliard方程的全局吸引子和分歧[J].四川师范大学学报(自然科学版),2020,43(01):56-60.[doi:10.3969/j.issn.1001-8395.2020.01.008]
 ZHANG Qiang,LI Limei.Global Attractor and Bifurcation for Convective Cahn-Hilliard Equation[J].Journal of SichuanNormal University,2020,43(01):56-60.[doi:10.3969/j.issn.1001-8395.2020.01.008]
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对流Cahn-Hilliard方程的全局吸引子和分歧()
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《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
43卷
期数:
2020年01期
页码:
56-60
栏目:
基础理论
出版日期:
2019-12-04

文章信息/Info

Title:
Global Attractor and Bifurcation for Convective Cahn-Hilliard Equation
文章编号:
1001-8395(2020)01-0056-05
作者:
张 强1 李俐玫2
1. 中国民用航空飞行学院 计算机学院, 四川 广汉 618307; 2. 四川师范大学 数学科学学院, 四川 成都 610066
Author(s):
ZHANG Qiang 1 LI Limei2
1.College of Computer Science, Civil Aviation Flight University of China, Guanghan 618307, Sichuan; 2.College of Mathematical Science, Sichuan Normal University, Chengdu 610066, Sichuan
关键词:
对流Cahn-Hilliard方程 全局吸引子 分歧 稳定性
Keywords:
convective Cahn-Hilliard equation global attractor bifurcation stability
分类号:
O175.2
DOI:
10.3969/j.issn.1001-8395.2020.01.008
文献标志码:
A
摘要:
利用吸引子分歧理论研究对流Cahn-Hilliard方程的动力学行为.当系统参数μ≤1时,稳态解u=0是全局稳定的,并且存在一个全局吸引子; 当μ>1时,稳定性从u=0转移到Ωμμ是从u=0分歧出的一个吸引子且同胚于S1.进一步,讨论Ωμ的拓扑结构和近似表达式.这些结果推广了一些已知结果.
Abstract:
In this paper, we will study the dynamical behavior of the convective Cahn-Hilliard equation by attractor bifurcation theory. If system parameter μ≤1, then steady state solution u=0 is globally stable, and there exists a global attractor. However, if μ>1, the stability switches from u=0 to an attractor Ωμ, which bifurcates from steady state u=0 and Ωμ is homeomorphic to S1. Moreover, the topological structure and the approximate expression of Ωμ are also discussed. These results generalize some known results.

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备注/Memo

备注/Memo:
收稿日期:2018-05-07 接受日期:2019-03-07 基金项目:国家自然科学基金(11701399) 第一作者简介: 张 强(1982—),男,副教授,主要从事偏微分方程与动力系统的研究,E-mail:zqcs007@163.com
更新日期/Last Update: 2019-12-04