各向异性表面能固体去湿的扩散界面法
A diffuse-interface approach for solid-state dewetting with anisotropic surface energies
摘要：
针对$d\in\{2,3\}$的${\mathbb R}^d$，提出了一种各向异性表面能固态去湿问题的扩散界面模型。引入的模型由各向异性的Cahn-Hilliard方程组成，具有光滑或双障碍势，以及退化的迁移率函数和适当的壁面边界条件。正则化后引入的扩散界面模型，并与适当的渐近展开的帮助下，我们恢复为尖锐的界面限制的各向异性表面扩散流的接口连同各向异性的杨氏定律和零通量条件在接触线的接口与一个固定的外部边界。此外，我们证明了正则化模型的弱解的存在性，光滑和障碍潜力。基于一个适当的有限元近似的数值结果表明，建议的扩散界面模型和尖锐的界面限制之间的良好协议。
英文摘要：
We present a diffuse-interface model for the solid-state dewetting problem with anisotropic surface energies in ${\mathbb R}^d$ for $d\in\{2,3\}$. The introduced model consists of the anisotropic Cahn--Hilliard equation, with either a smooth or a double-obstacle potential, together with a degenerate mobility function and appropriate boundary conditions on the wall. Upon regularizing the introduced diffuse-interface model, and with the help of suitable asymptotic expansions, we recover as the sharp-interface limit the anisotropic surface diffusion flow for the interface together with an anisotropic Young's law and a zero-flux condition at the contact line of the interface with a fixed external boundary. Furthermore, we show the existence of weak solutions for the regularized model, for both smooth and obstacle potential. Numerical results based on an appropriate finite element approximation are presented to demonstrate the excellent agreement between the proposed diffuse-interface model and its sharp-interface limit.
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