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

被引：17

作者：

Bonfoh, A ^{[1
]}

机构：

[1] Univ La Rochelle, Lab Math Calcul Asymptot, F-17042 Nantes 01, France

来源：

QUARTERLY OF APPLIED MATHEMATICS | 2006年 / 64卷 / 01期

关键词：

viscous Cahn-Hilliard equation; weighted Sobolev spaces; global attractor; Hausdorff dimension;

D O I：

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

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：93 / 104

页数：12

共 15 条

[1] EXISTENCE AND FINITE DIMENSIONALITY OF THE GLOBAL ATTRACTOR FOR EVOLUTION-EQUATIONS ON UNBOUNDED-DOMAINS [J].

ABERGEL, F .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1990, 83 (01) :85-108

[2] ESTIMATES NEAR THE BOUNDARY FOR SOLUTIONS OF ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS SATISFYING GENERAL BOUNDARY CONDITIONS .1. [J].

AGMON, S ;

DOUGLIS, A ;

NIRENBERG, L .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1959, 12 (04) :623-727

[3]

Babin A., 1995, Journal of Dynamics and Differential Equations, V7, P567, DOI 10.1007/BF02218725

[4]

Babin A. V., 1992, Journal of Dynamics and Differential Equations, V4, P555, DOI 10.1007/BF01048260

[5]

Babin A.V., 1992, ATTRACTORS EVOLUTION

[6] ATTRACTORS OF PARTIAL-DIFFERENTIAL EVOLUTION-EQUATIONS IN AN UNBOUNDED DOMAIN [J].

BABIN, AV ;

VISHIK, MI .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1990, 116 :221-243

[7] On Cahn-Hilliard-Gurtin equations [J].

Bonfoh, A ;

Miranville, A .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2001, 47 (05) :3455-3466

[8] ON SPINODAL DECOMPOSITION [J].

CAHN, JW .

ACTA METALLURGICA, 1961, 9 (09) :795-801

[9] FREE ENERGY OF A NONUNIFORM SYSTEM .1. INTERFACIAL FREE ENERGY [J].

CAHN, JW ;

HILLIARD, JE .

JOURNAL OF CHEMICAL PHYSICS, 1958, 28 (02) :258-267

[10]

Efendiev M, 1999, DISCRETE CONT DYN-A, V5, P399

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