On the n-Dimensional Porous Medium Diffusion Equation and Global Actions of the Symmetry Group

TL;DR

This paper explores the symmetry group actions on the n-dimensional porous medium diffusion equation, demonstrating how local symmetries can be extended globally through a special class of functions constructed via parabolic induction.

Contribution

It introduces a method to globalize local symmetry group actions for the porous medium equation using a novel class of functions derived from parabolic induction.

Findings

Global symmetry actions are achieved for the porous medium equation.

A new class of functions enabling globalization of symmetries is constructed.

The approach enhances understanding of symmetry structures in nonlinear diffusion equations.

Abstract

By restricting to a special class of smooth functions, the local action of the symmetry group is globalized. This special class of functions is constructed using parabolic induction.