On the Caginalp system with dynamic boundary conditions and singular potentials

被引：65

作者：

Cherfils, Laurence ^{[1
]}

Miranville, Alain ^{[2
]}

机构：

[1] Univ Rochelle, LMA, F-17042 La Rochelle, France

[2] Univ Poitiers, SP2MI, F-86962 Futuroscope, Chasseneuil, France

来源：

APPLICATIONS OF MATHEMATICS | 2009年 / 54卷 / 02期

关键词：

Caginalp phase field system; singular potential; dynamic boundary conditions; global existence; global attractor; Lojasiewicz-Simon inequality; convergence to a steady state; CAHN-HILLIARD EQUATION; LONG-TIME BEHAVIOR; PHASE-FIELD SYSTEM; ASYMPTOTIC-BEHAVIOR; CONVERGENCE; MODEL; EQUILIBRIUM; ATTRACTORS; REGULARITY;

D O I：

10.1007/s10492-009-0008-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article is devoted to the study of the Caginalp phase field system with dynamic boundary conditions and singular potentials. We first show that, for initial data in H (2), the solutions are strictly separated from the singularities of the potential. This turns out to be our main argument in the proof of the existence and uniqueness of solutions. We then prove the existence of global attractors. In the last part of the article, we adapt well-known results concerning the Lojasiewicz inequality in order to prove the convergence of solutions to steady states.

引用

页码：89 / 115

页数：27

共 33 条

[1] Convergence to equilibrium for the Cahn-Hilliard equation with a logarithmic free energy [J].