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arXiv · 1909.04458

Doubly Degenerate Diffuse Interface Models of Surface Diffusion

Marco Salvalaglio·Axel Voigt·Steven M. Wise
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Abstract

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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BibTeXRIS

Marco Salvalaglio, Axel Voigt, Steven M. Wise. 2019-09-10. Doubly Degenerate Diffuse Interface Models of Surface Diffusion. https://doi.org/10.1002/mma.7116

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