Exponential attractors and inertial manifolds for singular perturbations of the Cahn-Hilliard equations

Songmu Zheng, Albert Milani

Research output: Contribution to journalArticle

29 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 exponential attractors and inertial manifolds in the phase space H0 1(0,π)×H-1(0,π).

Original languageEnglish
Pages (from-to)843-877
Number of pages35
JournalNonlinear Analysis, Theory, Methods and Applications
Volume57
Issue number5-6
DOIs
Publication statusPublished - May 1 2004

Fingerprint

Inertial Manifolds
Exponential Attractors
Cahn-Hilliard Equation
Singular Perturbation
One Dimension
Boundary value problems
Phase Space
Dynamical systems
Dynamical system
Boundary Value Problem

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

@article{dd778aef823a4b33ab95545059035959,
title = "Exponential attractors and inertial manifolds 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 exponential attractors and inertial manifolds in the phase space H0 1(0,π)×H-1(0,π).",
author = "Songmu Zheng and Albert Milani",
year = "2004",
month = "5",
day = "1",
doi = "10.1016/j.na.2004.03.023",
language = "English",
volume = "57",
pages = "843--877",
journal = "Nonlinear Analysis, Theory, Methods and Applications",
issn = "0362-546X",
publisher = "Elsevier Limited",
number = "5-6",

}

Exponential attractors and inertial manifolds for singular perturbations of the Cahn-Hilliard equations. / Zheng, Songmu; Milani, Albert.

In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 57, No. 5-6, 01.05.2004, p. 843-877.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Exponential attractors and inertial manifolds for singular perturbations of the Cahn-Hilliard equations

AU - Zheng, Songmu

AU - Milani, Albert

PY - 2004/5/1

Y1 - 2004/5/1

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 exponential attractors and inertial manifolds in the phase space H0 1(0,π)×H-1(0,π).

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 exponential attractors and inertial manifolds in the phase space H0 1(0,π)×H-1(0,π).

UR - http://www.scopus.com/inward/record.url?scp=2542500465&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2542500465&partnerID=8YFLogxK

U2 - 10.1016/j.na.2004.03.023

DO - 10.1016/j.na.2004.03.023

M3 - Article

AN - SCOPUS:2542500465

VL - 57

SP - 843

EP - 877

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

IS - 5-6

ER -