Lie Symmetry Analysis of 3D Unsteady Diffusion and Reaction-Diffusion with Singularities

Subject Areas : International Journal of Mathematical Modelling & Computations

Yadollah AryaNejad ^{1 *} , Mehdi Jafari ² , Razieh Mirzanand ³

1 - Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, I.R. of Iran
2 - Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, I.R. of Iran
3 - Institute of advanced studies, Payame Noor University, P.O. Box 19395-3697, Tehran, I.R. of Iran.

Received: 2023-10-01 Accepted : 2023-12-27 Published : 2024-11-15

Keywords: 3D reaction-diffusion equation, Optimal system, Reduction equations, Symmetry group, Lie algebras.,

Abstract :

In this study, we apply the basic Lie symmetry method to investigate of transient three dimensional (3D) reaction-diffusion equation with singularities. We obtain the classical Lie symmetries for the equation under consideration. Therefore, we respond to the question of classification of the equation symmetries and, as a result, derived the infinitesimal symmetries and thirteen basic combinations of vector fields which are used to reduce the order of the given equation. We create the optimal system of Lie subalgebras and the symmetry reductions of the considered equation.