Doubly degenerate diffuse interface models of surface diffusion
Doubly degenerate diffuse interface models of surface diffusion
复制标题
DOI：
10.1002/mma.7116
复制
发表时间：
2019-09
影响因子：
2.9
通讯作者：
M. Salvalaglio;A. Voigt;S. Wise
中科院分区：
文献类型：
--
作者：
M. Salvalaglio;A. Voigt;S. Wise
我们讨论了两个用于各向同性表面扩散的双重退化的卡恩 - 希利厄德（DDCH）模型。在迁移率函数以及与化学势相关的约束函数中都引入了退化。我们的计算结果表明，约束函数能对表面扩散给出更精确的近似。我们考虑对一个之前出现过的模型进行略微推广，该模型是非变分的，这意味着沿着解的轨迹没有明显的能量耗散。我们还引入了一个新的变分模型，更确切地说，是一个能量耗散模型，它可与广义的非变分模型相关联。对于这两个模型，我们使用形式匹配渐近法来证明其收敛到表面扩散的锐界面极限。
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.