Group properties and invariant solutions of a sixth-order thin film equation in viscous fluid

摘要

Using group theoretical methods, we analyze the generalization of aone-dimensional sixth-order thin film equation which arises in considering themotion 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 andinvariant solutions are constructed. It is found that some similarity solutionsare of great physical interest such as sink and source solutions,travelling-wave solutions, waiting-time solutions, and blow-up solutions.