University of Tabriz Computational Methods for Differential Equations 2345-3982 7 1 2019 01 01 Symmetry group, Hamiltonian equations and conservation laws of general three-dimensional anisotropic non-linear sourceless heat transfer equation 54 68 8082 EN Seyed Reza Hejazi Department of mathematical sciences, Shahrood university of technology, Shahrood, Semnan, Iran Elaheh Saberi Department of mathematical sciences, Shahrood university of technology, Shahrood, Semnan, Iran Elham Lashkarian Department of mathematical sciences, Shahrood university of technology, Shahrood, Semnan, Iran Journal Article 2017 10 24 ‎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. https://cmde.tabrizu.ac.ir/article_8082_ce59954b9985ed275b6bcae07e350a29.pdf