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Volume 22, Issue 5
Force Convergence for the de Gennes-Cahn-Hilliard Energy

Shibin Dai, Abba Ramadan & Joseph Renzi

DOI: 10.4208/ijnam2025-1032

Int. J. Numer. Anal. Mod., 22 (2025), pp. 745-754.

Published online: 2025-05

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  • 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.

  • Keywords

de Gennes-Cahn-Hilliard energy, Gamma convergence, force convergence.

  • AMS Subject Headings

35B40, 35J20, 35J60, 35Q92

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{IJNAM-22-745, author = {Dai , ShibinRamadan , Abba and Renzi , Joseph}, title = {Force Convergence for the de Gennes-Cahn-Hilliard Energy }, journal = {International Journal of Numerical Analysis and Modeling}, year = {2025}, volume = {22}, number = {5}, pages = {745--754}, 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.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2025-1032}, url = {http://global-sci.org/intro/article_detail/ijnam/24084.html} }
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 -

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.

Dai , ShibinRamadan , Abba and Renzi , Joseph. (2025). Force Convergence for the de Gennes-Cahn-Hilliard Energy . International Journal of Numerical Analysis and Modeling. 22 (5). 745-754. doi:10.4208/ijnam2025-1032
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