Finite-dimensional attractor for the viscous Cahn-Hilliard equation in an unbounded domain

Ahmed Bonfoh

doi:10.1090/S0033-569X-06-00988-3

Finite-dimensional attractor for the viscous Cahn-Hilliard equation in an unbounded domain

Ahmed Bonfoh^*

^*Corresponding author for this work

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

17 Scopus citations

Abstract

We consider the viscous Cahn-Hilliard equation in an infinite domain. Due to the noncompactness of operators, we use weighted Sobolev spaces to prove that the semigroup generated by this equation has the global attractor which has finite Hausdorff dimension.

Original language	English
Pages (from-to)	93-104
Number of pages	12
Journal	Quarterly of Applied Mathematics
Volume	64
Issue number	1
DOIs	https://doi.org/10.1090/S0033-569X-06-00988-3
State	Published - Mar 2006
Externally published	Yes

Keywords

Global attractor
Hausdorff dimension
Viscous Cahn-Hilliard equation
Weighted Sobolev spaces

ASJC Scopus subject areas

Applied Mathematics

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10.1090/S0033-569X-06-00988-3

Cite this

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title = "Finite-dimensional attractor for the viscous Cahn-Hilliard equation in an unbounded domain",

abstract = "We consider the viscous Cahn-Hilliard equation in an infinite domain. Due to the noncompactness of operators, we use weighted Sobolev spaces to prove that the semigroup generated by this equation has the global attractor which has finite Hausdorff dimension.",

keywords = "Global attractor, Hausdorff dimension, Viscous Cahn-Hilliard equation, Weighted Sobolev spaces",

author = "Ahmed Bonfoh",

year = "2006",

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N2 - We consider the viscous Cahn-Hilliard equation in an infinite domain. Due to the noncompactness of operators, we use weighted Sobolev spaces to prove that the semigroup generated by this equation has the global attractor which has finite Hausdorff dimension.

AB - We consider the viscous Cahn-Hilliard equation in an infinite domain. Due to the noncompactness of operators, we use weighted Sobolev spaces to prove that the semigroup generated by this equation has the global attractor which has finite Hausdorff dimension.

KW - Global attractor

KW - Hausdorff dimension

KW - Viscous Cahn-Hilliard equation

KW - Weighted Sobolev spaces

UR - https://www.scopus.com/pages/publications/33645953289

U2 - 10.1090/S0033-569X-06-00988-3

DO - 10.1090/S0033-569X-06-00988-3

M3 - Article

AN - SCOPUS:33645953289

SN - 0033-569X

VL - 64

SP - 93

EP - 104

JO - Quarterly of Applied Mathematics

JF - Quarterly of Applied Mathematics

IS - 1

ER -

Finite-dimensional attractor for the viscous Cahn-Hilliard equation in an unbounded domain

Abstract

Keywords

ASJC Scopus subject areas

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