Symmetry group, Hamiltonian equations and conservation laws of general three-dimensional anisotropic non-linear sourceless heat transfer equation

Abstract

‎In this paper Lie point symmetries‎, ‎Hamiltonian equations and conservation‎ ‎laws of general three-dimensional anisotropic non-linear sourceless heat transfer‎ ‎equation are investigated‎. ‎First of all Lie symmetries are obtained by using the general method‎ based on invariance condition of a system of differential equations under a pro‎longed vector field‎. ‎Then the structure of symmetry operators as a Lie algebra are clarified and the classification of subalgebras under adjoint transformation is given‎. ‎Hamiltonian equations including Hamiltonian symmetry are obtained‎. ‎Finally a modified virsion of Noether's method including the direct method are applied in order to find local conservation laws of the equation‎.