Long-time behavior of the Cahn–Hilliard equation with dynamic boundary condition

被引：0
作者：
Alain Miranville
Hao Wu
机构：
[1] Université de Poitiers,Laboratoire de Mathématiques et Applications, UMR CNRS 7348, SP2MI, Boulevard Marie et Pierre Curie
[2] Fudan University,Téléport 2
来源：
Journal of Elliptic and Parabolic Equations | 2020年 / 6卷
关键词：
Cahn–Hilliard equation; Dynamic boundary condition; Global attractor; Exponential attractor; 35K35; 35K60; 35B40; 35B41; 37L30;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study the long-time behavior, within the framework of infinite dimensional dynamical systems, of the Cahn–Hilliard equation endowed with a new class of dynamic boundary conditions. The system under investigation was recently derived by Liu–Wu (Arch Ration Mech Anal 233:167–247, 2019) via an energetic variational approach such that it naturally fulfills physical properties like mass conservation, energy dissipation and force balance. For the system with regular potentials, we prove the existence of exponential attractors, which also yields the existence of a global attractor with finite fractal dimension. For the system with singular potentials, we obtain the existence of a global attractor in a suitable complete metric space.
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页码：283 / 309
页数：26
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