viscous fluid中六阶薄膜方程的群性质和不变解
Group properties and invariant solutions of a sixth-order thin film equation in viscous fluid
摘要：
利用群论方法，我们分析了一维六阶薄膜方程的推广，该方程是在考虑由上覆弹性板驱动的粘性流体薄膜的运动时产生的。给出了点对称的最一般李群分类及其李代数和等价群。类似的减少进行和不变的解决方案构造。结果发现，一些相似的解决方案，如汇和源的解决方案，行波解决方案，等待时间的解决方案，和爆破解决方案是非常有趣的物理。
英文摘要：
Using group theoretical methods, we analyze the generalization of a one-dimensional sixth-order thin film equation which arises in considering the motion of a thin film of viscous fluid driven by an overlying elastic plate. The most general Lie group classification of point symmetries, its Lie algebra, and the equivalence group are obtained. Similar reductions are performed and invariant solutions are constructed. It is found that some similarity solutions are of great physical interest such as sink and source solutions, travelling-wave solutions, waiting-time solutions, and blow-up solutions.
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