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

*(English)*Zbl 1424.35126Summary: 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 |