Recent Results on the Cahn - Hilliard Equation with Dynamic Boundary Conditions

P. Colli;  ; G. Gilardi; J. Sprekels;  ;

doi:10.14529/mmp170101

Recent Results on the Cahn - Hilliard Equation with Dynamic Boundary Conditions

Bulletin of the South Ural State University Series Mathematical Modelling Programming and Computer Software ◽

10.14529/mmp170101 ◽

2017 ◽

Vol 10 (1) ◽

pp. 5-21

Author(s):

P. Colli ◽

◽

G. Gilardi ◽

J. Sprekels ◽

◽

...

Keyword(s):

Boundary Conditions ◽

Dynamic Boundary Conditions ◽

Hilliard Equation ◽

Dynamic Boundary ◽

Cahn Hilliard Equation

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Energy Law Preserving Finite Element Scheme for the Cahn-Hilliard Equation with Dynamic Boundary Conditions†

Communications in Computational Physics ◽

10.4208/cicp.2019.js60.14 ◽

2019 ◽

Vol 26 (5) ◽

pp. 1490-1509

Author(s):

Na Li

Keyword(s):

Finite Element ◽

Boundary Conditions ◽

Dynamic Boundary Conditions ◽

Finite Element Scheme ◽

Element Scheme ◽

Hilliard Equation ◽

Dynamic Boundary ◽

Cahn Hilliard Equation ◽

Energy Law

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Finite-volume method for the Cahn-Hilliard equation with dynamic boundary conditions

ESAIM Proceedings and Surveys ◽

10.1051/proc/201445052 ◽

2014 ◽

Vol 45 ◽

pp. 502-511

Author(s):

Flore Nabet

Keyword(s):

Boundary Conditions ◽

Finite Volume Method ◽

Finite Volume ◽

Dynamic Boundary Conditions ◽

Hilliard Equation ◽

Dynamic Boundary ◽

Cahn Hilliard Equation ◽

Volume Method

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Exponential attractors for the Cahn-Hilliard equation with dynamic boundary conditions

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.590 ◽

2005 ◽

Vol 28 (6) ◽

pp. 709-735 ◽

Cited By ~ 70

Author(s):

A. Miranville ◽

S. Zelik

Keyword(s):

Boundary Conditions ◽

Dynamic Boundary Conditions ◽

Exponential Attractors ◽

Hilliard Equation ◽

Dynamic Boundary ◽

Cahn Hilliard Equation

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Convergence to equilibrium for the Cahn–Hilliard equation with dynamic boundary conditions

Journal of Differential Equations ◽

10.1016/j.jde.2004.05.004 ◽

2004 ◽

Vol 204 (2) ◽

pp. 511-531 ◽

Cited By ~ 54

Author(s):

Hao Wu ◽

Songmu Zheng

Keyword(s):

Boundary Conditions ◽

Convergence To Equilibrium ◽

Dynamic Boundary Conditions ◽

Hilliard Equation ◽

Dynamic Boundary ◽

Cahn Hilliard Equation

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The Cahn-Hilliard equation with singular potentials and dynamic boundary conditions

Discrete and Continuous Dynamical Systems ◽

10.3934/dcds.2010.28.275 ◽

2010 ◽

Vol 28 (1) ◽

pp. 275-310 ◽

Cited By ~ 34

Author(s):

Alain Miranville ◽

◽

Sergey Zelik ◽

Keyword(s):

Boundary Conditions ◽

Singular Potentials ◽

Dynamic Boundary Conditions ◽

Hilliard Equation ◽

Dynamic Boundary ◽

Cahn Hilliard Equation

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Cahn–Hilliard equation with dynamic boundary conditions and mass constraint on the boundary

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2015.04.057 ◽

2015 ◽

Vol 429 (2) ◽

pp. 1190-1213 ◽

Cited By ~ 32

Author(s):

Pierluigi Colli ◽

Takeshi Fukao

Keyword(s):

Boundary Conditions ◽

Dynamic Boundary Conditions ◽

Hilliard Equation ◽

Dynamic Boundary ◽

Mass Constraint ◽

Cahn Hilliard Equation

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Maximal regularity and asymptotic behavior of solutions for the Cahn–Hilliard equation with dynamic boundary conditions

Annali di Matematica Pura ed Applicata (1923 -) ◽

10.1007/s10231-005-0175-3 ◽

2006 ◽

Vol 185 (4) ◽

pp. 627-648 ◽

Cited By ~ 41

Author(s):

Jan Prüss ◽

Reinhard Racke ◽

Songmu Zheng

Keyword(s):

Asymptotic Behavior ◽

Boundary Conditions ◽

Maximal Regularity ◽

Asymptotic Behavior Of Solutions ◽

Dynamic Boundary Conditions ◽

Hilliard Equation ◽

Dynamic Boundary ◽

Cahn Hilliard Equation

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Non-isothermal viscous Cahn-Hilliard equation with inertial term and dynamic boundary conditions

Communications on Pure & Applied Analysis ◽

10.3934/cpaa.2014.13.1855 ◽

2014 ◽

Vol 13 (5) ◽

pp. 1855-1890 ◽

Cited By ~ 6

Author(s):

Cecilia Cavaterra ◽

◽

Maurizio Grasselli ◽

Hao Wu ◽

◽

...

Keyword(s):

Boundary Conditions ◽

Inertial Term ◽

Dynamic Boundary Conditions ◽

Hilliard Equation ◽

Dynamic Boundary ◽

Cahn Hilliard Equation

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Finite-Volume Analysis for the Cahn-Hilliard Equation with Dynamic Boundary Conditions

Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects - Springer Proceedings in Mathematics & Statistics ◽

10.1007/978-3-319-05684-5_39 ◽

2014 ◽

pp. 401-409 ◽

Cited By ~ 2

Author(s):

Flore Nabet

Keyword(s):

Boundary Conditions ◽

Finite Volume ◽

Dynamic Boundary Conditions ◽

Volume Analysis ◽

Hilliard Equation ◽

Dynamic Boundary ◽

Cahn Hilliard Equation

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An error estimate for a finite-volume scheme for the Cahn–Hilliard equation with dynamic boundary conditions

Numerische Mathematik ◽

10.1007/s00211-021-01230-7 ◽

2021 ◽

Vol 149 (1) ◽

pp. 185-226

Author(s):

Flore Nabet

Keyword(s):

Boundary Conditions ◽

Error Estimate ◽

Finite Volume ◽

Finite Volume Scheme ◽

Dynamic Boundary Conditions ◽

Volume Scheme ◽

Hilliard Equation ◽

Dynamic Boundary ◽

Cahn Hilliard Equation

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