| 具浓度相关迁移率和梯度相关位势的一维Cahn-Hilliard方程 |
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| 引用本文： | 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]. 吉林大学学报(理学版), 2009, 47(6): 1140-1144 |
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| 作者姓名： | 徐辽沙 黄锐 高天玲 |
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| 作者单位： | 吉林大学,数学学院,长春,130012;深圳大学,数学与计算科学学院,广东,深圳,518060 |
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| 基金项目： | 国家自然科学基金,教育部博士学科点专项科研基金 |
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| 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.
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| 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 |
| 收稿时间： | 2009-03-05 |
One Dimensional Cahn-Hilliard Equation with Concentration Dependent Mobility and Gradient Dependent Potential |
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| XU Liao-sha,HUANG Rui,GAO Tian-ling. One Dimensional Cahn-Hilliard Equation with Concentration Dependent Mobility and Gradient Dependent Potential[J]. Journal of Jilin University: Sci Ed, 2009, 47(6): 1140-1144 |
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| Authors: | XU Liao-sha HUANG Rui GAO Tian-ling |
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| Affiliation: | 1. College of Mathematics, Jilin University, Changchun 130012, China;2. College of Mathematics and Computational Science, Shenzhen University, Shenzhen 518060, Guangdong Province, China |
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| 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. |
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| Keywords: | Cahn-Hilliard equation concentration dependent mobility gradient dependent potential existence and uniqueness of solution |
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