Surface tension, higher order phase field equations, dimensional analysis and Clairaut’s equation

AIMS Mathematics

Gunduz Caginalp¹ 

关键词: : ;    surface tension;    phase field equations;    Clairaut’s equation;    homogeneous functions;    dimensional analysis;   

DOI  :  10.3934/Math.2017.2.207

学科分类：数学（综合）

来源: AIMS Press

【 摘 要 】

A higher order phase field free energy leads to higher order differential equations. The surface tension involves L² norms of higher order derivatives. An analysis of dimensionless variables shows that the surface tension satisfies a Clairaut’s equation in terms of the coeffcients of the higher order phase field equations. The Clairaut’s equation can be solved by characteristics on a suitable surface in the R^N space of coeffcients. This perspective may also be regarded as interpreting dimensional analysis through Clairaut’s equation. The surface tension is shown to be a homogeneous function of monomials of the coeffcients.

【 授权许可】

CC BY