| 具浓度相关黏性系数的黏性Cahn-Hilliard方程解的爆破性 |
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| 引用本文： | 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].吉林大学学报(理学版),2011,49(3):471-474. |
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| 作者姓名： | 黄锐 王泽佳 |
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| 作者单位： | 1. 华南师范大学 数学科学学院, 广州 510631,2. 吉林大学 数学学院, 长春 130012 |
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| 基金项目： | 国家自然科学基金，教育部博士点基金，教育部留学回国人员科研启动基金，吉林大学基本科研业务平台基地建设项目 |
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| 摘 要： | 研究具浓度相关黏性系数的黏性Cahn-Hilliard方程解的爆破性质. 利用能量估计方法, 在关于黏性系数的两个不同结构性条件下分别证明了初边值问题的解在有限时刻爆破和时间趋于无穷时解趋于无穷两个性质. 结果表明, 黏性系数所满足的结构性条件对于方程的解有较大影响.
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| 关 键 词： | 爆破 黏性Cahn-Hilliard方程 浓度相关黏性系数 |
| 收稿时间： | 2010-11-29 |
Blow-Up of Solutions to the Viscous Cahn-Hilliard Equation with Concentration Dependent Viscosity |
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| HUANG Rui,WANG Ze-jia.Blow-Up of Solutions to the Viscous Cahn-Hilliard Equation with Concentration Dependent Viscosity[J].Journal of Jilin University: Sci Ed,2011,49(3):471-474. |
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| Authors: | HUANG Rui WANG Ze-jia |
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| Institution: | 1. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China;2. College of Mathematics, Jilin University, Changchun 130012, China |
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| Abstract: | We studied the blow up of the solutions to the viscous Cahn Hilliard equation with concentration dependent viscosity. The results show that the structural conditons satisfied by the coefficient of viscosity play an important role in the properties of the solutions. Under two different structural conditions of the coefficient of viscosity, usingthe energy method, we proved that the solutions of the initial boundary value problem blow up in finite time or tend to infinity as t→+∞. |
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| Keywords: | blow up viscous Cahn Hilliard equation concentration dependent viscosity |
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