Global attractors for singular perturbations of the Cahn-Hilliard equations

被引：58

作者：

Zheng, SM

Milani, A ^{[1
]}

机构：

[1] Univ Wisconsin, Dept Math, Milwaukee, WI 53211 USA

[2] Fudan Univ, Inst Math, Shanghai 200433, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2005年 / 209卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Cahn-Hilliard equations; singular perturbation; semiflow; global attractor; upper semicontinuity;

D O I：

10.1016/j.jde.2004.08.026

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the singular perturbations of two boundary value problems, concerning respectively the viscous and the nonviscous Cahn-Hilliard equations in one dimension of space. We show that the dynamical systems generated by these two problems admit global attractors in the phase space H-0(1) (0, pi) x H-1 (0, pi), and that these global attractors are at least upper-semicontinuous with respect to the vanishing of the perturbation parameter. (C) 2004 Elsevier Inc. All rights reserved.

引用

页码：101 / 139

页数：39

共 50 条

[1] Exponential attractors and inertial manifolds for singular perturbations of the Cahn-Hilliard equations
Zheng, SM
Milani, A
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2004, 57 (5-6) : 843 - 877
[2] Global attractors for Cahn-Hilliard equations with nonconstant mobility
Schimperna, Giulio
NONLINEARITY, 2007, 20 (10) : 2365 - 2387
[3] Robust exponential attractors for Cahn-Hilliard type equations with singular potentials
Miranville, A
Zelik, S
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2004, 27 (05) : 545 - 582
[4] Cahn-Hilliard vs Singular Cahn-Hilliard Equations in Phase Field Modeling
Zhang, Tianyu
Wang, Qi
COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2010, 7 (02) : 362 - 382
[5] Global attractors for the 2D hyperbolic Cahn-Hilliard equations
Khanmamedov, Azer
Yayla, Sema
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2018, 69 (01):
[6] UPPER SEMICONTINUITY OF GLOBAL ATTRACTORS FOR THE PERTURBED VISCOUS CAHN-HILLIARD EQUATIONS
Kania, Maria B.
TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2008, 32 (02) : 327 - 345
[7] CAHN-HILLIARD VS SINGULAR CAHN-HILLIARD EQUATIONS IN SIMULATIONS OF IMMISCIBLE BINARY FLUIDS
Chen, Lizhen
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2018, 8 (04): : 1050 - 1060
[8] ON THE CAHN-HILLIARD/ALLEN-CAHN EQUATIONS WITH SINGULAR POTENTIALS
Miranville, Alain
Saoud, Wafa
Talhouk, Raafat
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2019, 24 (08): : 3633 - 3651
[9] Global Attractors for the Initial Value Problems of Cahn－Hilliard Equations on Compact Manifolds
郭柏灵，王友德
数学进展, 1994, (01) : 91 - 92
[10] Well-Posedness and Global Attractors for Viscous Fractional Cahn-Hilliard Equations with Memory
Ozturk, Eylem
Shomberg, Joseph L.
FRACTAL AND FRACTIONAL, 2022, 6 (09)

← 1 2 3 4 5 →