Supercaloric functions for the porous medium equation

TL;DR

This paper investigates the behavior of unbounded supersolutions to the porous medium equation in slow diffusion, distinguishing two types based on local integrability of the pressure and exploring their implications.

Contribution

It introduces a criterion based on pressure integrability to classify supersolutions and discusses the resulting differences in their properties.

Findings

Supersolutions are classified into two types based on pressure integrability.

The criterion impacts the understanding of supersolution behavior.

Implications for the analysis of slow diffusion processes.

Abstract

In the slow diffusion case unbounded supersolutions of the porous medium equation are of two totally different types, depending on whether the pressure is locally integrable or not. This criterion and its consequences are discussed.