北京航空航天大学学报 ›› 1998, Vol. 24 ›› Issue (5): 584-587.

• 论文 • 上一篇    下一篇

Cahn-Hilliard方程的行波解

刘深泉, 陆启韶, 王琪   

  1. 北京航空航天大学 应用数理系
  • 收稿日期:1997-03-12 发布日期:2010-11-18
  • 作者简介:男 33岁 博士生 100083 北京
  • 基金资助:

    国家自然科学基金(19572014)资助项目

Traveling Waves of the Cahn-Hilliard Equation

Liu Shenquan, Lu Qishao, Wang Qi   

  1. Beijing University of Aeronautics and Astronautics,Dept. of Applied Mathematics and Physics
  • Received:1997-03-12 Published:2010-11-18

摘要: 主要利用奇异摄动方法,得到一维Cahn-Hilliard方程行波解形式的内、外解.两者匹配得到整体行波解.这个结果的特点是,它不仅将高阶偏微分方程的解用内外解匹配好,而且完全满足方程的边界条件和初始条件.当长时间变化时, Cahn-Hilliard方程的解以行波结构为极限状态.此结果很好地解释Cahn-Hilliard方程的现有理论及数值结果,实际模型和方程的性质也完全符合.

Abstract: The asymptotic perturbation method is used to deal with the Cahn-Hilliard equation and obtain the inner and outer solutions of traveling waves. The two solutions are matched into one solution of the equation. The feature of the method not only matches the inner and outer solutions of the higher order partial differential equation, but also satisfies the boundary condition and initial condition. After a long time evolution, the solutions of the Cahn-Hillard equation have the structures of traveling waves as the limit states. The result in this paper can explain the theoretic and numerical simulation results of the Cahn-Hillard equation. The property of model fits well with that of the equation.

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