Force Convergence for the de Gennes-Cahn-Hilliard Energy

Abstract

The degenerate de Gennes-Cahn-Hilliard (dGCH) equation is a recent phase field model that may more accurately approximate surface diffusion. After establishing the Gamma convergence of the dGCH energy in [10], in this paper, we study the convergence of boundary force. This is done by carefully crafting a nonlinear transformation that transforms the dGCH energy into a Cahn-Hilliard-type energy with a non-smooth potential. We carry out explicit computations and analysis to this new system, which in turn enables us to establish the convergence of boundary force for the dGCH energy.