Hejazi, Seyed Reza; Saberi, Elaheh; Lashkarian, Elham Symmetry group, Hamiltonian equations and conservation laws of general three-dimensional anisotropic non-linear sourceless heat transfer equation. (English) Zbl 1424.35126 Comput. Methods Differ. Equ. 7, No. 1, 54-68 (2019). Summary: 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 version of Noether’s method including the direct method are applied in order to find local conservation laws of the equation. MSC: 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 76M60 Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics Keywords:heat transfer equation; Lie symmetry; partial differential equation; Hamiltonian equations; conservation laws PDF BibTeX XML Cite \textit{S. R. Hejazi} et al., Comput. Methods Differ. Equ. 7, No. 1, 54--68 (2019; Zbl 1424.35126) Full Text: Link