具浓度相关迁移率和梯度相关位势的一维Cahn-Hilliard方程

摘要

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.%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.