Department of Mathematics, Baylor University
One Bear Place \#97328
Waco, TX 76798-7328, USA
email: Mark_Sepanski@baylor.edu
Mark R. Sepanski
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.
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Mark R. Sepanski Department of Mathematics, Baylor University One Bear Place \#97328 Waco, TX 76798-7328, USA email: Mark_Sepanski@baylor.edu |
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