此文为读书报告，主要参考On the Cahn-Hilliard Equation一文，主要内容如下。 Cahn-Hilliard方程是一类重要的高阶非线性扩散方程，它来源于自然界中广泛存在的扩散现象，如热力学中两相物质之间相互扩散现象，生物种群的竞争与排斥现象，河床迁移的过程等。在过去的几十年中，国内外众多的学者对这类方程进行了广泛的研究。早在1958 年，J.W.Cahn和J.Hilliard在研究热力学中两相物质之间相互扩散现象时就提出了此类方程。在扩散过程中，与时间相关的模型就可以用Cahn-Hilliard方程来描述，因此对该方程做出一些介绍就显得相关重要了。 本文首先对Cahn-Hilliard方程做一个简单的介绍，紧接着对方程解的整体存在性和有限时刻爆破性做出讨论，最后解决了Galerkin有限元近似相关的问题。

This is a book report; refer to the article On the Cahn-Hilliard Equation, the main content is as follows. Cahn-Hilliard equation is an important class of higher order nonlinear diffusion equation, which comes from the spread of the phenomenon, is widespread in nature, such as the thermodynamics between the two-phase material interdiffusion phenomenon, competition and exclusion of the biological populations, the river bed migration the process, etc. In the past few decades, many scholars at home and abroad for such equations has been extensively studied. As early as in 1958, J.W.Cahn and J.Hilliard in research in material thermodynamics two phase between diffusion phenomenon and put forward the equation. In the diffusion process, and time related model can use Cahn-Hilliard equation to describe, so the equation to make some introduction is related to the important. First of all, we make a simple introduction to the Cahn-Hilliard equation, followed by the differential equation solution global existence and blow-up in finite time of discussion, finally we solve the problems relate to the finite element Galerkin approximation.