STRUCTURE-PRESERVING FINITE DIFFERENCE SCHEMES FOR THE CAHN HILLIARD EQUATION WITH DYNAMIC BOUNDARY CONDITIONS IN THE ONE-DIMENSIONAL CASE
STRUCTURE-PRESERVING FINITE DIFFERENCE SCHEMES FOR THE CAHN HILLIARD EQUATION WITH DYNAMIC BOUNDARY CONDITIONS IN THE ONE-DIMENSIONAL CASE
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DOI：
10.3934/cpaa.2017093
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发表时间：
2017-09-01
影响因子：
1
通讯作者：
Wada, Saori
中科院分区：
文献类型：
--
作者：
Fukao, Takeshi;Yoshikawa, Shuji;Wada, Saori
研究了具有动态边界条件的一维Cahn Hilliard方程的保结构差分格式。动态边界条件是一种包含时间导数的传输条件，即它本身就是一个时间演化方程。具有动态边界条件的Cahn Hilliard方程从不同的角度得到了很好的处理。标准类型由序参数的动态边界条件和化学势的Neumann边界条件组成。最近，Goldstein Miranville Schperna为Cahn Hilliard方程提出了一种新的动态边界条件。本文介绍了这两种动态边界条件下的数值格式。此外，对于原边界条件，还得到了具有误差估计的格式解的存在性的一个数学结果。
The structure-preserving finite difference schemes for the one dimensional Cahn Hilliard equation with dynamic boundary conditions are studied. A dynamic boundary condition is a sort of transmission condition that includes the time derivative, namely, it is itself a time evolution equation. The Cahn Hilliard equation with dynamic boundary conditions is well-treated from various viewpoints. The standard type consists of a dynamic boundary condition for the order parameter, and the Neumann boundary condition for the chemical potential. Recently, Goldstein Miranville Schimperna proposed a new type of dynamic boundary condition for the Cahn Hilliard equation. In this article, numerical schemes for the problem with these two kinds of dynamic boundary conditions are introduced. In addition, a mathematical result on the existence of a solution for the scheme with an error estimate is also obtained for the former boundary condition.