Ergodicity for singular-degenerate porous media equations

TL;DR

This paper investigates the long-term behavior of solutions to stochastic porous media equations with degenerate nonlinearities, establishing the existence and uniqueness of invariant measures using the lower-bound method.

Contribution

It introduces a novel analysis of ergodicity for degenerate porous media equations with self-organised criticality, proving invariant measure existence and uniqueness.

Findings

Existence of invariant measure established

Uniqueness of invariant measure proved

Analysis applicable to self-organised criticality models

Abstract

The long time behaviour of solutions to generalised stochastic porous media equations on bounded domains with Dirichlet boundary data is studied. We focus on a degenerate form of nonlinearity arising in self-organised criticality. Based on the so-called lower-bound method, the existence and uniqueness of an invariant measure is proved.