THE CAHN-HILLIARD EQUATION WITH SINGULAR POTENTIALS AND DYNAMIC BOUNDARY CONDITIONS

被引：63

作者：

Miranville, Alain ^{[1
]}

Zelik, Sergey ^{[2
]}

机构：

[1] Univ Poitiers, Lab Math & Applicat, SP2MI, F-86962 Futuroscope, France

[2] Univ Surrey, Dept Math, Guildford GU2 7XH, Surrey, England

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2010年 / 28卷 / 01期

关键词：

Cahn-Hilliard equation; dynamic boundary conditions; singular potentials; variational solutions; separation from the singularities; global attractor; exponential attractors; EXPONENTIAL ATTRACTORS; SPINODAL DECOMPOSITION; ASYMPTOTIC-BEHAVIOR; HIGHER DIMENSIONS; CONVERGENCE; SYSTEM; EQUILIBRIUM; CONTACT; MODES; TIME;

D O I：

10.3934/dcds.2010.28.275

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Our aim in this paper is to study the Cahn-Hilliard equation with singular potentials and dynamic boundary conditions. In particular, we prove, owing to proper approximations of the singular potential and a suitable notion of variational solutions, the existence and uniqueness of solutions. We also discuss the separation of the solutions from the singularities of the potential. Finally, we prove the existence of global and exponential attractors.

引用

页码：275 / 310

页数：36

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