具浓度相关迁移率和梯度相关位势的一维Cahn-Hilliard方程

J4 ›› 2009, Vol. 47 ›› Issue (6): 1140-1144.

具浓度相关迁移率和梯度相关位势的一维Cahn-Hilliard方程

徐辽沙¹, 黄锐¹, 高天玲²

1. 吉林大学数学学院, 长春 130012|2. 深圳大学数学与计算科学学院, 广东深圳 518060

收稿日期:2009-03-05 出版日期:2009-11-26 发布日期:2010-01-07
通讯作者: 黄锐 E-mail:huang@jlu.edu.cn.

One Dimensional CahnHilliard Equation with ConcentrationDependent Mobility and Gradient Dependent Potential

XU Liao sha¹, HUANG Rui¹, GAO Tianling²

1. College of Mathematics, Jilin University, Changchun 130012, China;2. College of Mathematics and Computational Science, Shenzhen University, Shenzhen 518060, Guangdong Province, China

Received:2009-03-05 Online:2009-11-26 Published:2010-01-07
Contact: HUANG Rui E-mail:huang@jlu.edu.cn.

摘要/Abstract

摘要：

利用LeraySchauder不动点定理证明一类具浓度相关迁移率和梯度相关位势的一维Cahn-Hilliard方程古典解的存在性, 并利用共轭法证明了相应问题解的惟一性. 在一维情形下推广了已有的关于具常迁移率和梯度相关位势的Cahn-Hilliard方程初边值问题的结果.

关键词: Cahn-Hilliard方程, 浓度相关迁移率, 梯度相关位势, 解的存在惟一性

Abstract:

We used the LeraySchauder fixed point theorem to prove the existence of the classical solutions of the initial boundary
value problem of one dimensional CahnHilliard equation with concentration dependent mobility and gradient dependent potential, and showed the uniqueness of the solutions by means of Holmgren’s approach. In the case of one dimension, we generalized our previous work on the corresponding problem of the Cahn-Hilliard equation with constant mobility and gradient dependent potential.

Key words: CahnHilliard equation, concentration dependent mobility, gradient dependent potential, existence and uniqueness of solution

中图分类号:

O175.4

徐辽沙, 黄锐, 高天玲. 具浓度相关迁移率和梯度相关位势的一维Cahn-Hilliard方程[J]. J4, 2009, 47(6): 1140-1144.

XU Liao sha, HUANG Rui, GAO Tianling. One Dimensional CahnHilliard Equation with ConcentrationDependent Mobility and Gradient Dependent Potential[J]. J4, 2009, 47(6): 1140-1144.

[1]	贾秀利, 关丽红, 闫龙. α-稳定噪声驱动随机CahnHilliard方程解的存在唯一性[J]. 吉林大学学报(理学版), 2014, 52(06): 1151-1154.
[2]	黄锐, 王泽佳. 具浓度相关黏性系数的黏性Cahn-Hilliard方程解的爆破性[J]. J4, 2011, 49(03): 471-474.
[3]	柴世民, 尹云光, 宫成春, 尹丽. 一类Cahn-Hilliard方程弱解的存在惟一性[J]. J4, 2008, 46(03): 453-456.