标题： Allen-Cahn方程与Cahn-Hilliard型动态边界条件的渐近分析 显示英文标题

标题： Asymptotic analysis of the Allen-Cahn equation with dynamic boundary conditions of Cahn-Hilliard type

摘要： 与动态边界条件耦合的偏微分方程问题可以看作是体和其边界之间的传输问题。 对于热方程和Allen-Cahn方程，本文研究了具有动态边界条件的各种形式的问题。 在体内的Cahn-Hilliard方程情况下，已经提出了几种模型，其中边界方程和条件有所不同。 最近，已经在这些模型中的多个模型中研究了消失的表面扩散极限。 在这种情况下，得到的动态边界方程通常采用前向后向抛物方程的形式。 在本文中，我们关注一个不同的模型，在该模型中，Allen-Cahn方程控制体的动力学，而边界条件为Cahn-Hilliard型。 我们分析了系统的渐近行为，包括极限问题的适定性以及解之间的差异相应的误差估计。 这些方面针对三种类型的极限系统进行了讨论。 显示英文摘要

摘要： Problems for partial differential equations coupled with dynamic boundary conditions can be viewed as a type of transmission problem between the bulk and its boundary. For the heat equation and the Allen-Cahn equation, various forms of such problems with dynamic boundary conditions are studied in this paper. In the case of the Cahn-Hilliard equation in the bulk, several models have been proposed in which the boundary equations and conditions differ. Recently, the vanishing surface diffusion limit has been investigated in more than one of these models. In such settings, the resulting dynamic boundary equation typically takes the form of a forward-backward parabolic equation. In this paper, we focus on a different model, in which the Allen-Cahn equation governs the bulk dynamics, while the boundary condition is of Cahn-Hilliard type. We analyze the asymptotic behavior of the system, including the well-posedness of the limiting problems and corresponding error estimates for the differences between solutions. These aspects are discussed for three types of limiting systems.