Selfsimilar Equivalence of Porous Medium and p-Laplacian Flows

TL;DR

This paper establishes a connection between the porous medium equation and the p-Laplacian equation by demonstrating their equivalence through selfsimilar solutions, providing new insights into nonlinear diffusion models.

Contribution

It shows the equivalence of two major nonlinear diffusion models at the level of selfsimilar solutions, a novel theoretical link between these equations.

Findings

Porous medium and p-Laplacian equations are equivalent in selfsimilar form.

Selfsimilar solutions serve as a bridge between the two models.

The result enhances understanding of nonlinear diffusion processes.

Abstract

We demonstrate the equivalence between the two popular models of nonlinear diffusion, the porous medium equation and the p-Laplacian equation. The equivalence is shown at the level of selfsimilar solutions.