%0 Journal Article %T Symmetry group, Hamiltonian equations and conservation laws of general three-dimensional anisotropic non-linear sourceless heat transfer equation %J Computational Methods for Differential Equations %I University of Tabriz %Z 2345-3982 %A Hejazi, Seyed Reza %A Saberi, Elaheh %A Lashkarian, Elham %D 2019 %\ 01/01/2019 %V 7 %N 1 %P 54-68 %! Symmetry group, Hamiltonian equations and conservation laws of general three-dimensional anisotropic non-linear sourceless heat transfer equation %K ‎Heat transfer equation %K Lie symmetry %K Partial differential‎ equation %K Hamiltonian equations %K Conservation laws‎ %R %X ‎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. %U https://cmde.tabrizu.ac.ir/article_8082_ce59954b9985ed275b6bcae07e350a29.pdf