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

Songmu Zheng; Albert Milani

doi:10.1016/j.na.2004.03.023

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

Songmu Zheng
, Albert Milani

Mathematics & Statistical Sciences

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

33 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 H₀¹(0,π)×H^-1(0,π).

Original language	English
Pages (from-to)	843-877
Number of pages	35
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	57
Issue number	5-6
DOIs	https://doi.org/10.1016/j.na.2004.03.023
Publication status	Published - May 2004

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1016/j.na.2004.03.023

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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 H01(0,π)×H-1(0,π).",

author = "Songmu Zheng and Albert Milani",

year = "2004",

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journal = "Nonlinear Analysis, Theory, Methods and Applications",

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

AU - Zheng, Songmu

AU - Milani, Albert

PY - 2004/5

Y1 - 2004/5

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 H01(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 H01(0,π)×H-1(0,π).

UR - https://www.scopus.com/pages/publications/2542500465

UR - https://www.scopus.com/pages/publications/2542500465#tab=citedBy

U2 - 10.1016/j.na.2004.03.023

DO - 10.1016/j.na.2004.03.023

M3 - Article

AN - SCOPUS:2542500465

SN - 0362-546X

VL - 57

SP - 843

EP - 877

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 5-6

ER -

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

Abstract

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