Convergence to steady states of solutions of the Cahn-Hilliard and Caginalp equations with dynamic boundary conditions

被引：109

作者：

Chill, Ralph

Fasangova, Eva

Pruess, Jan

机构：

[1] Univ Ulm, Abt Angiol Anal, D-89069 Ulm, Germany

[2] Charles Univ, Dept Math Anal, Prague 18675 8, Czech Republic

[3] Univ Halle Wittenberg, Fach Math & Informat, D-06120 Halle, Germany

来源：

MATHEMATISCHE NACHRICHTEN | 2006年 / 279卷 / 13-14期

关键词：

Cahn-Hilliard equation; Caginalp problem; convergence to steady states; Lojasiewicz-Simon inequality;

D O I：

10.1002/mana.200410431

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a solution of the Cahn-Hilliard equation or an associated Caginalp problem with dynamic boundary condition in the case of a general potential and prove that under some conditions on the potential it converges, as t --> infinity, to a stationary solution. The main tool will be the Lojasiewicz-Simon inequality for the underlying energy functional. (C) 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

引用

页码：1448 / 1462

页数：15

共 22 条

[1] SPECTRAL COMPARISON PRINCIPLES FOR THE CAHN-HILLIARD AND PHASE-FIELD EQUATIONS, AND TIME SCALES FOR COARSENING [J].