Convergence to equilibrium for the Cahn-Hilliard equation with a logarithmic free energy

被引：107

作者：

Abels, Helmut

Wilke, Mathias

机构：

[1] Max Planck Inst Math Sci, D-04103 Leipzig, Germany

[2] Univ Halle Wittenberg, Inst Anal, Fachbereich Math Informat, D-06099 Halle, Saale, Germany

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2007年 / 67卷 / 11期

关键词：

Cahn-Hilliard equation; monotone operators; logarithmic potential; Lojasiewicz-Simon inequality; convergence to steady states;

D O I：

10.1016/j.na.2006.10.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we investigate the asymptotic behavior of the nonlinear Cahn-Hilliard equation with a logarithmic free energy and similar singular free energies. We prove an existence and uniqueness result with the help of monotone operator methods, which differs from the known proofs based on approximation by smooth potentials. Moreover, we apply the Lojasiewicz-Simon inequality to show that each solution converges to a steady state as time tends to infinity. (c) 2006 Elsevier Ltd. All rights reserved.

引用

页码：3176 / 3193

页数：18

共 22 条

[1] A fourth-order parabolic equation with a logarithmic nonlinearity [J].