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A sixth order Cahn-Hilliard type equation arising in oil-water-surfactant mixtures. (English) Zbl 1229.35108
Summary: 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.

MSC:
35K52Higher-order parabolic systems, initial boundary value problems
35K60Nonlinear initial value problems for linear parabolic equations
35Q70PDEs in connection with mechanics of particles and systems
35L20Second order hyperbolic equations, boundary value problems