American Institute of Mathematical Sciences

November  2011, 10(6): 1823-1847. doi: 10.3934/cpaa.2011.10.1823

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

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

Received  June 2010 Revised  April 2011 Published  May 2011

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.
Citation: Irena Pawłow, Wojciech M. Zajączkowski. A sixth order Cahn-Hilliard type equation arising in oil-water-surfactant mixtures. Communications on Pure & Applied Analysis, 2011, 10 (6) : 1823-1847. doi: 10.3934/cpaa.2011.10.1823
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