具浓度相关迁移率和梯度相关位势的一维Cahn-Hilliard方程  

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

作　　者：徐辽沙[1] 黄锐[1] 高天玲[2] 

机构地区：[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

出　　处：《吉林大学学报（理学版）》2009年第6期1140-1144,共5页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:10826041J0630104);教育部博士学科点专项科研基金(批准号:200801831002)

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-H illiard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-H illiard方程初边值问题的结果.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.

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 

分 类 号：O175.4[理学—数学]