This article is devoted to the study of the asymptotic behavior of aCaginalp phase-field system with nonlinear dynamic boundary conditions. As a proper parameter ε goes to zero, this problem converges to the viscous Cahn-Hilliard equation. We firstprove the existence and uniqueness of the solution to the system and then provide an upper semicontinuous family of globalattractors A_ε . Furthermore, we prove the existence of anexponential attractor for each problem, which yields, since it contains the aforementioned global attractor, the finite fractal dimensionality of A_ε.

Asymptotic behavior of a phase-field system with dynamic boundary conditions / Gatti, Stefania; Miranville, A.. - STAMPA. - 251:(2006), pp. 149-170.

Asymptotic behavior of a phase-field system with dynamic boundary conditions

GATTI, Stefania;
2006

Abstract

This article is devoted to the study of the asymptotic behavior of aCaginalp phase-field system with nonlinear dynamic boundary conditions. As a proper parameter ε goes to zero, this problem converges to the viscous Cahn-Hilliard equation. We firstprove the existence and uniqueness of the solution to the system and then provide an upper semicontinuous family of globalattractors A_ε . Furthermore, we prove the existence of anexponential attractor for each problem, which yields, since it contains the aforementioned global attractor, the finite fractal dimensionality of A_ε.
2006
Differential equations: inverse and direct problems, Lect. Notes Pure Appl. Math.
9781584886044
Taylor and Francis
STATI UNITI D'AMERICA
Asymptotic behavior of a phase-field system with dynamic boundary conditions / Gatti, Stefania; Miranville, A.. - STAMPA. - 251:(2006), pp. 149-170.
Gatti, Stefania; Miranville, A.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/461845
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