Stability of the two- and three-dimensional kink solutions to the Cahn-Hilliard equation

被引:3
作者
Bettinson, D
Rowlands, G
机构
[1] Department of Physics, University of Warwick, Coventry, Warwick
来源
PHYSICAL REVIEW E | 1997年 / 55卷 / 05期
关键词
D O I
10.1103/PhysRevE.55.5427
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 ; 080103 ; 080704 ;
摘要
We give an analysis of the Cahn-Hilliard equation, which admits both cylindrically and spherically symmetric, stationary kink solutions. Since analytic expressions for these solutions are unobtainable in closed form, we devise an approximate method of solution taking the radius as large and scaling variables in its reciprocal. To lowest order, the solution is that of the one-dimensional kink solution which has been analyzed in earlier work. In this paper we begin by investigating the stability of the cylindrically symmetric kink solution to small perturbations involving angular and z dependence. It is found that the solution is stable to perturbations involving angular variation, but is unstable to a general perturbation. We go on to show that the spherically symmetric kink solution is stable to all small perturbations.
引用
收藏
页码:5427 / 5432
页数:6
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