Phase-field systems with nonlinear coupling and dynamic boundary conditions

被引：28

作者：

Cavaterra, Cecilia ^{[2
]}

Gal, Ciprian G. ^{[3
]}

Grasselli, Maurizio ^{[1
]}

Miranville, Alain ^{[4
]}

机构：

[1] Politecn Milan, Dipartimento Matemat F Brioschi, I-20133 Milan, Italy

[2] Univ Milan, Dipartimento Matemat T Enriques, I-20133 Milan, Italy

[3] Univ Missouri, Dept Math, Columbia, MO 65211 USA

[4] Univ Poitiers, Lab Math & Applicat, CNRS, SP2MI,UMR 6086, F-86962 Futuroscope, France

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2010年 / 72卷 / 05期

关键词：

Phase-field equations; Dynamic boundary conditions; Laplace-Beltrami operator; Global attractors; Exponential attractors; Lojasiewicz-Simon inequality; Convergence to equilibrium; CAHN-HILLIARD EQUATION; LONG-TIME BEHAVIOR; EXPONENTIAL ATTRACTORS; ASYMPTOTIC-BEHAVIOR; CAGINALP SYSTEM; MODEL;

D O I：

10.1016/j.na.2009.11.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider phase-field systems of Caginalp type on a three-dimensional bounded domain. The order parameter fulfills a dynamic boundary condition, while the (relative) temperature is subject to a homogeneous boundary condition of Dirichlet, Neumann or Robin type. Moreover, the two equations are nonlinearly coupled through a quadratic growth function. Here we extend several results which have been proven by some of the authors for the linear coupling. More precisely, we demonstrate the existence and uniqueness of global solutions. Then we analyze the associated dynamical system and we establish the existence of global as well as exponential attractors. We also discuss the convergence of given Solutions to a single equilibrium. (C) 2009 Elsevier Ltd. All rights reserved.

引用

页码：2375 / 2399

页数：25

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