Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 101, pp. 1-24.

Title: Nonlinear potential filtration equation and global
       actions of Lie symmetries

Author: Mark R. Sepanski (Baylor Univ., Waco, TX, USA)

Abstract:
 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.
 
Submitted June 11, 2009. Published August 21, 2009.
Math Subject Classifications: 35A30.
Key Words: Lie symmetry; nonlinear potential filtration equation; 
           global action.