Symmetry Classication and Invariance of the Reynolds Equation

In this essay, extensions to the results of Lie symmetry classication of Reynolds equation are proposed. The innitesimal tech- nique is used to derive symmetry groups of the Reynolds equation. One- dimensional optimal system is constructed for symmetry sub-algebras gained through Lie point symmetry. At the end, the general symmetry group of the non-conservative generalized thin-lm equation are deter- mined.