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

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.