Derivation of the fractional porous medium equation from a microscopic dynamics

TL;DR

This paper derives the fractional porous medium equation as a hydrodynamic limit from a microscopic particle system with long-range interactions and occupancy-dependent jump rates.

Contribution

It introduces a novel derivation of the fractional porous medium equation from microscopic dynamics with occupancy-dependent jump rates.

Findings

Fractional porous medium equation derived from microscopic particle system.

Long-range interactions modeled via fractional Laplacian.

Occupancy-dependent jump rates influence the macroscopic limit.

Abstract

In this article we derive the fractional porous medium equation for any power of the fractional Laplacian as the hydrodynamic limit of a microscopic dynamics of random particles with long range interactions, but the jump rate highly depends on the occupancy near the sites where the interactions take place.