Nonlinear potential filtration equation and global actions of Lie symmetries

The Lie point symmetries of the nonlinear potential filtration equation break into five cases. Contact symmetries provide another two cases. By restricting to a natural class of functions, we show that these symmetries exponentiate to a global action of the corresponding Lie group in four of the cases of Lie point symmetries. Furthermore, the action is actually the composition of a linear action with a simple translation. In fact, as a crucial step in applying the machinery of representation theory, this is accomplished using induced representations. In the remaining case as well as the contact symmetries, we show that the infinitesimal action does not exponentiate to any global Lie group action on any reasonable space of functions.