Global attractors for singular perturbations of the Cahn-Hilliard equations

Songmu Zheng, Albert Milani

Research output: Contribution to journalArticle

38 Citations (Scopus)

Abstract

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 H0l (0, π) × H-1 (0, π), and that these global attractors are at least upper-semicontinuous with respect to the vanishing of the perturbation parameter.

Original languageEnglish
Pages (from-to)101-139
Number of pages39
JournalJournal of Differential Equations
Volume209
Issue number1
DOIs
Publication statusPublished - Feb 1 2005

Fingerprint

Cahn-Hilliard Equation
Global Attractor
Singular Perturbation
Boundary value problems
Dynamical systems
Upper Semicontinuous
Parameter Perturbation
One Dimension
Phase Space
Dynamical system
Boundary Value Problem

All Science Journal Classification (ASJC) codes

  • Analysis

Cite this

@article{dacb1672356b4ac9bc0c92a6b106ea4f,
title = "Global attractors for singular perturbations of the Cahn-Hilliard equations",
abstract = "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 H0l (0, π) × H-1 (0, π), and that these global attractors are at least upper-semicontinuous with respect to the vanishing of the perturbation parameter.",
author = "Songmu Zheng and Albert Milani",
year = "2005",
month = "2",
day = "1",
doi = "10.1016/j.jde.2004.08.026",
language = "English",
volume = "209",
pages = "101--139",
journal = "Journal of Differential Equations",
issn = "0022-0396",
publisher = "Academic Press Inc.",
number = "1",

}

Global attractors for singular perturbations of the Cahn-Hilliard equations. / Zheng, Songmu; Milani, Albert.

In: Journal of Differential Equations, Vol. 209, No. 1, 01.02.2005, p. 101-139.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Global attractors for singular perturbations of the Cahn-Hilliard equations

AU - Zheng, Songmu

AU - Milani, Albert

PY - 2005/2/1

Y1 - 2005/2/1

N2 - 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 H0l (0, π) × H-1 (0, π), and that these global attractors are at least upper-semicontinuous with respect to the vanishing of the perturbation parameter.

AB - 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 H0l (0, π) × H-1 (0, π), and that these global attractors are at least upper-semicontinuous with respect to the vanishing of the perturbation parameter.

UR - http://www.scopus.com/inward/record.url?scp=10944240024&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=10944240024&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2004.08.026

DO - 10.1016/j.jde.2004.08.026

M3 - Article

VL - 209

SP - 101

EP - 139

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 1

ER -