Document Type : Research Paper
Department of mathematical sciences, Shahrood university of technology, Shahrood, Semnan, Iran
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.