On the extension of Lie group analysis to functional differential equations

Marta Wacławczyk, Martin Oberlack

Archives of Mechanics

58, 2006, 597-618

In the present paper the classical point symmetry analysis is extended from partial differential to functional differential equations. In order to perform the group analysis and deal with the functional derivatives, we extend the quantities such as infinitesimal transformations, prolongations and invariant solutions. For the sake of example, the procedure is applied to the functional formulation of the Burgers equation. The method can further lead to important applications in continuum mechanics.