Cahn-Hilliard equation on the boundary with bulk condition of Allen-Cahn type

被引：4

作者：

Colli, Pierluigi ^{[1
]}

Fukao, Takeshi ^{[2
]}

机构：

[1] Univ Pavia, Dipartimento Matemat, Via Ferrata 1, I-27100 Pavia, Italy

[2] Kyoto Univ Educ, Fac Educ, Dept Math, Fushimi Ku, 1 Fujinomori, Kyoto 6128522, Japan

来源：

ADVANCES IN NONLINEAR ANALYSIS | 2020年 / 9卷 / 01期

关键词：

Cahn-Hilliard equation; bulk condition; dynamic boundary condition; well-posedness; POTENTIALS; SYSTEM; MODEL;

D O I：

10.1515/anona-2018-0055

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The well-posedness of a system of partial differential equations with dynamic boundary conditions is discussed. This system is a sort of transmission problem between the dynamics in the bulk Omega and on the boundary Gamma. The Poisson equation for the chemical potential and the Allen-Cahn equation for the order parameter in the bulk Omega are considered as auxiliary conditions for solving the Cahn-Hilliard equation on the boundary G. Recently, the well-posedness of this equation with a dynamic boundary condition, both of Cahn-Hilliard type, was discussed. Based on this result, the existence of the solution and its continuous dependence on the data are proved.

引用

页码：16 / 38

页数：23

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