Preliminarily group classification of a class of 2D nonlinear heat equations

TL;DR

This paper applies the Lie method to perform a preliminary group classification of a class of 2D nonlinear heat equations, demonstrating the use of algebraic techniques in symmetry analysis.

Contribution

It introduces the preliminary group classification method to analyze 2D nonlinear heat equations, expanding the application of algebraic approaches in symmetry classification.

Findings

Classification of symmetries for the equations

Identification of special cases with enhanced symmetry

Demonstration of algebraic approach effectiveness

Abstract

A preliminary group classification of the class 2D nonlinear heat equations $u_t=f(x,y,u,u_x,u_y)(u_{xx}+u_{yy})$, where $f$ is arbitrary smooth function of the variables $x,y,u,u_x$ and $u_y$ using Lie method, is given. The paper is one of the few applications of an algebraic approach to the problem of group classification: the method of preliminary group classification.