Global Dynamics of the Cahn-Hilliard/Allen-Cahn Equation

被引：0

作者：

Ma, Mingze ^{[1
]}

Zhao, Xiaopeng ^{[1
]}

机构：

[1] Northeastern Univ, Coll Sci, Shenyang 110004, Peoples R China

来源：

JOURNAL OF MATHEMATICAL STUDY | 2023年 / 56卷 / 02期

关键词：

Global attractor; Cahn-Hilliard; Allen-Cahn; absorbing set; LONG-TIME BEHAVIOR; EXISTENCE;

D O I：

10.4208/jms.v56n2.23.04

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider the global dynamics of the Cahn-Hilliard/AllenCahn equation with periodic boundary value conditions in 2D bounded domain n. We show that the equation has a global attractor in Hp4er(n) when the initial value belongs to Hp1er(n).

引用

页码：156 / 172

页数：17

共 16 条

[1] The Cahn-Hilliard Equation with Logarithmic Potentials
Cherfils, Laurence
Miranville, Alain
Zelik, Sergey
[J]. MILAN JOURNAL OF MATHEMATICS, 2011, 79 (02) : 561 - 596
[2] Dlotko T., 1993, DIFFER EQU DYN SYST, V1, P137
[3] ELLIOTT CM, 1986, ARCH RATION MECH AN, V96, P339
[4] A Cahn-Hilliard model in bounded domains with permeable walls
Gal, Ciprian G.
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2006, 29 (17) : 2009 - 2036
[5] Israel H, 2012, J APPL ANAL COMPUT, V2, P29
[6] WELL-POSEDNESS AND LONG TIME BEHAVIOR OF AN ALLEN-CAHN TYPE EQUATION
Israel, Haydi
[J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2013, 12 (06) : 2811 - 2827
[7] The role of multiple microscopic mechanisms in cluster interface evolution
Karali, Georgia
Katsoulakis, Markos A.
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2007, 235 (02) : 418 - 438
[8] ON THE EXISTENCE OF SOLUTION FOR A CAHN-HILLIARD/ALLEN-CAHN EQUATION
Karali, Georgia
Nagase, Yuko
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2014, 7 (01): : 127 - 137
[9] On the convergence of a fourth order evolution equation to the Allen-Cahn equation
Karali, Georgia
Ricciardi, Tonia
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (11) : 4271 - 4281
[10] EXISTENCE OF PERIODIC SOLUTION FOR A CAHN-HILLIARD/ALLEN-CAHN EQUATION IN TWO SPACE DIMENSIONS
Liu, Changchun
Tang, Hui
[J]. EVOLUTION EQUATIONS AND CONTROL THEORY, 2017, 6 (02): : 219 - 237

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