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

‎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 di erential equations under a prolonged vector eld. Then the structure of symmetry operators as a Lie algebra are clari ed and the classi cation of subalgebras under adjoint transformation is given. Hamiltonian equations including Hamiltonian symmetry are obtained. Finally a modi ed version of Noether s method including the direct method are applied in order to nd local conservation laws of the equation.