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.


35K52 Initial-boundary value problems for higher-order parabolic systems
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35Q70 PDEs in connection with mechanics of particles and systems of particles
35L20 Initial-boundary value problems for second-order hyperbolic equations
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