论文标题
材料转移的相位场动力学：cahn--hilliard方程与反应速率依赖性动态边界条件
Phase-field dynamics with transfer of materials: The Cahn--Hilliard equation with reaction rate dependent dynamic boundary conditions
论文作者
论文摘要
cahn--hilliard方程是描述两种材料混合物的相分离过程的最常见模型之一。为了更好地描述材料与边界之间的短距离相互作用，近期已经提出并研究了Cahn--Hilliard方程的各种动态边界条件。特别感兴趣的是Goldstein，Miranville和Schimperna的模型（Physica d，2011）和Liu and Wu的模型（Arch。这两个模型都具有相似的物理特性，但其质量保护行为有很大差异。在本文中，我们介绍了一个新模型，该模型在这些先前模型之间进行了插值，并研究了分析性能，例如在弱和强烈意义上都提到的上述模型的存在和收敛到上述模型。对于强烈的融合，我们还根据插值参数建立了速率，这些插值参数由新插值模型的完全离散，无条件稳定和有限的有限元方案获得的数值模拟支持。
The Cahn--Hilliard equation is one of the most common models to describe phase separation processes of a mixture of two materials. For a better description of short-range interactions between the material and the boundary, various dynamic boundary conditions for the Cahn--Hilliard equation have been proposed and investigated in recent times. Of particular interests are the model by Goldstein, Miranville and Schimperna (Physica D, 2011) and the model by Liu and Wu (Arch.~Ration.~Mech.~Anal., 2019). Both of these models satisfy similar physical properties but differ greatly in their mass conservation behaviour. In this paper we introduce a new model which interpolates between these previous models, and investigate analytical properties such as the existence of unique solutions and convergence to the previous models mentioned above in both the weak and the strong sense. For the strong convergences we also establish rates in terms of the interpolation parameter, which are supported by numerical simulations obtained from a fully discrete, unconditionally stable and convergent finite element scheme for the new interpolation model.
