The Cahn-Hilliard equation serves as an important diffuse interface model for the dynamics of binary mixtures. In this talk, we discuss a new class of dynamic boundary condition for the Cahn-Hilliard equation that accounts for nontrivial short-range interactions near the solid wall. Then we present some results on the well-posedness and long-time behavior of the initial boundary value problem under suitable assumptions on the potential functions.

 

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