Cahn-Hilliard 方程的行波解

Traveling Waves of the Cahn Hilliard Equation

主要利用奇异摄动方法，得到一维ＣａｈｎＨｉｌｉａｒｄ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Ｈｉｌｉａｒｄ方程的解以行波结构为极限状态．此结果很好地解释ＣａｈｎＨｉｌｉａｒｄ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．

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.