2D viscoelastic equation from the perspective of Lie groups

We investigate 2-dimensional viscoelastic equations with a view of Lie groups. In this sense, we answer question of the symmetry classification. We provide the algebra of symmetry and build the optimal system of Lie subalgebras. Reductions of similarities related to subalgebras are classified. In the end by using Bluman-Anco homotopy formula, we find local conservation laws of the viscoelastic equation.