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

Mathematics Department University of Pittsburgh, Pittsburgh, PA 15260, USA

Special Issue: Nonlinear Evolution PDEs, Interfaces and Applications

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 RN 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.
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Keywords surface tension; phase field equations; Clairaut’s equation; homogeneous functions; dimensional analysis

Citation: Gunduz Caginalp. Surface tension, higher order phase field equations, dimensional analysis and Clairaut’s equation. AIMS Mathematics, 2017, 2(2): 207-214. doi: 10.3934/Math.2017.2.195


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