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We discuss two doubly degenerate Cahn–Hilliard (DDCH) models for isotropic surface diffusion. Degeneracy is introduced in both the mobility function and a restriction function associated to the chemical potential. Our computational results suggest that the restriction functions yield more accurate approximations of surface diffusion. We consider a slight generalization of a model that has appeared before, which is non‐variational, meaning there is no clear energy that is dissipated along the solution trajectories. We also introduce a new variational and, more precisely, energy dissipative model, which can be related to the generalized non‐variational model. For both models, we use formal matched asymptotics to show the convergence to the sharp‐interface limit of surface diffusion.
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Doubly degenerate diffuse interface models of anisotropic surface diffusion
We extend the doubly degenerate Cahn–Hilliard (DDCH) models for isotropic surface diffusion, which yield more accurate approximations than classical degenerate Cahn–Hilliard (DCH) models, to the anisotropic case. We consider both weak and strong anisotropies and demonstrate the capabilities of the approach for these cases numerically. The proposed model provides a variational and energy dissipative approach for anisotropic surface diffusion, enabling large‐scale simulations with material‐specific parameters.
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- Award ID(s):
- 2012634
- PAR ID:
- 10452158
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Mathematical Methods in the Applied Sciences
- Volume:
- 44
- Issue:
- 7
- ISSN:
- 0170-4214
- Page Range / eLocation ID:
- p. 5406-5417
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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