论文标题
具有前向动态边界条件和非平滑电势的Cahn-Hilliard系统
A Cahn-Hilliard system with forward-backward dynamic boundary condition and non-smooth potentials
论文作者
论文摘要
考虑了具有方程式和动态边界条件的Cahn-Hilliard类型的系统。该系统来自在Liu-Wu（Arch。Mech。Mech。Anal。233（2019），167--247）中进行的推导。实际上，相关问题可以看作是批量中相位变量的传输问题，边界上的相应变量。研究了作用在边界相变量上的表面扩散系数的渐近行为被研究为0。通过此分析，我们在极限处获得了前向后动态边界条件。我们可以处理具有双孔结构的一般电位，包括非平滑双凸电势。我们说明，极限问题也通过证明连续的依赖估计值充分。此外，如果在批量和边界上的两个图显示相同的增长时，我们表明限制问题的解更加规则，并且我们证明了对于扩散参数的合适顺序的错误估计。
A system with equation and dynamic boundary condition of Cahn-Hilliard type is considered. This system comes from a derivation performed in Liu-Wu (Arch. Ration. Mech. Anal. 233 (2019), 167--247) via an energetic variational approach. Actually, the related problem can be seen as a transmission problem for the phase variable in the bulk and the corresponding variable on the boundary. The asymptotic behavior as the coefficient of the surface diffusion acting on the boundary phase variable goes to 0 is investigated. By this analysis we obtain a forward-backward dynamic boundary condition at the limit. We can deal with a general class of potentials having a double-well structure, including the non-smooth double-obstacle potential. We illustrate that the limit problem is well-posed by also proving a continuous dependence estimate. Moreover, in the case when the two graphs, in the bulk and on the boundary, exhibit the same growth, we show that the solution of the limit problem is more regular and we prove an error estimate for a suitable order of the diffusion parameter.
