TY - JOUR
T1 - Force Convergence for the de Gennes-Cahn-Hilliard Energy 
AU - Dai , Shibin
AU - Ramadan , Abba
AU - Renzi , Joseph
JO - International Journal of Numerical Analysis and Modeling
VL - 5
SP - 745
EP - 754
PY - 2025
DA - 2025/05
SN - 22
DO - http://doi.org/10.4208/ijnam2025-1032
UR - https://global-sci.org/intro/article_detail/ijnam/24084.html
KW - de Gennes-Cahn-Hilliard energy, Gamma convergence, force convergence.
AB - <p style="text-align: justify;">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.</p>