A sixth order Cahn-Hilliard type equation arising in oil-water-surfactant mixtures

Irena Pawłow; Wojciech M. Zajączkowski

doi:10.3934/cpaa.2011.10.1823

Article Contents

2011, Volume 10, Issue 6: 1823-1847. Doi: 10.3934/cpaa.2011.10.1823

This issue Previous Article Nonexistence of nonconstant global minimizers with limit at $\infty$ of semilinear elliptic equations in all of $R^N$ Next Article

A sixth order Cahn-Hilliard type equation arising in oil-water-surfactant mixtures

Irena Pawłow^1, and
Wojciech M. Zajączkowski^2,

1.
Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01-447 Warsaw
2.
Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warsaw

Received: May 31, 2010

Revised: March 31, 2011

Published: October 2011

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Abstract

An initial-boundary-value problem for the sixth order Cahn-Hilliard type equation in 3-D is studied. The problem describes phase transition dynamics in ternary oil-water-surfactant systems. It is based on the Landau-Ginzburg theory proposed for such systems by G. Gompper et al. We prove that the problem under consideration is well posed in the sense that it admits a unique global smooth solution which depends continuously on the initial datum.

Keywords:

Sixth order Cahn-Hilliard type equation,
existence of strong global solutions,
oil-water-surfactant systems.

Mathematics Subject Classification: Primary: 35K50, 35K60; Secondary: 35Q72, 35L205.

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References

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