Singularly perturbed 1D Cahn-Hilliard equation revisited

Ahmed Bonfoh; Maurizio Grasselli; Alain Miranville

doi:10.1007/s00030-010-0075-0

Singularly perturbed 1D Cahn-Hilliard equation revisited

Ahmed Bonfoh^*, Maurizio Grasselli, Alain Miranville

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

25 Scopus citations

Abstract

We consider a singular perturbation of the one-dimensional Cahn-Hilliard equation subject to periodic boundary conditions. We construct a family of exponential attractors { M_ε}, ε ≥ 0 being the perturbation parameter, such that the map ε M_ε is Hölder continuous. Besides, the continuity at ε = 0 is obtained with respect to a metric independent of ε Continuity properties of global attractors and inertial manifolds are also examined.

Original language	English
Pages (from-to)	663-695
Number of pages	33
Journal	Nonlinear Differential Equations and Applications
Volume	17
Issue number	6
DOIs	https://doi.org/10.1007/s00030-010-0075-0
State	Published - Dec 2010

Keywords

Cahn-Hilliard equations
Global attractors
Inertial manifolds
Robust exponential attractors
Singular perturbations

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1007/s00030-010-0075-0

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title = "Singularly perturbed 1D Cahn-Hilliard equation revisited",

abstract = "We consider a singular perturbation of the one-dimensional Cahn-Hilliard equation subject to periodic boundary conditions. We construct a family of exponential attractors \{ Mε\}, ε ≥ 0 being the perturbation parameter, such that the map ε Mε is H{\"o}lder continuous. Besides, the continuity at ε = 0 is obtained with respect to a metric independent of ε Continuity properties of global attractors and inertial manifolds are also examined.",

keywords = "Cahn-Hilliard equations, Global attractors, Inertial manifolds, Robust exponential attractors, Singular perturbations",

author = "Ahmed Bonfoh and Maurizio Grasselli and Alain Miranville",

year = "2010",

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doi = "10.1007/s00030-010-0075-0",

language = "English",

volume = "17",

pages = "663--695",

journal = "Nonlinear Differential Equations and Applications",

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TY - JOUR

T1 - Singularly perturbed 1D Cahn-Hilliard equation revisited

AU - Bonfoh, Ahmed

AU - Grasselli, Maurizio

AU - Miranville, Alain

PY - 2010/12

Y1 - 2010/12

N2 - We consider a singular perturbation of the one-dimensional Cahn-Hilliard equation subject to periodic boundary conditions. We construct a family of exponential attractors { Mε}, ε ≥ 0 being the perturbation parameter, such that the map ε Mε is Hölder continuous. Besides, the continuity at ε = 0 is obtained with respect to a metric independent of ε Continuity properties of global attractors and inertial manifolds are also examined.

AB - We consider a singular perturbation of the one-dimensional Cahn-Hilliard equation subject to periodic boundary conditions. We construct a family of exponential attractors { Mε}, ε ≥ 0 being the perturbation parameter, such that the map ε Mε is Hölder continuous. Besides, the continuity at ε = 0 is obtained with respect to a metric independent of ε Continuity properties of global attractors and inertial manifolds are also examined.

KW - Cahn-Hilliard equations

KW - Global attractors

KW - Inertial manifolds

KW - Robust exponential attractors

KW - Singular perturbations

UR - https://www.scopus.com/pages/publications/78249258379

U2 - 10.1007/s00030-010-0075-0

DO - 10.1007/s00030-010-0075-0

M3 - Article

AN - SCOPUS:78249258379

SN - 1021-9722

VL - 17

SP - 663

EP - 695

JO - Nonlinear Differential Equations and Applications

JF - Nonlinear Differential Equations and Applications

IS - 6

ER -

Singularly perturbed 1D Cahn-Hilliard equation revisited

Abstract

Keywords

ASJC Scopus subject areas

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