# Lattice model for Fast Diffusion Equation

## TL;DR

This paper derives a fast diffusion equation as a limit of a zero-range process, revealing how microscopic particle interactions lead to macroscopic fast diffusion behavior, and discusses convergence properties of numerical methods.

## Contribution

It introduces a lattice-based zero-range process model that converges to a fast diffusion equation, providing a new microscopic foundation for the PDE and analyzing numerical convergence.

## Key findings

- Derivation of FDE as a scaling limit of zero-range processes
- Identification of conditions for fast diffusion from microscopic models
- Results on convergence of the method of lines for FDE

## Abstract

We obtain a fast diffusion equation (FDE) as scaling limit of a sequence of zero-range process with symmetric unit rate. Fast diffusion effect comes from the fact that the diffusion coefficient goes to infinity as the density goes to zero. Therefore, in order to capture the behaviour for an arbitrary small density of particles, we consider a proper rescaling of a model with a typically high number of particles per site. Furthermore, we obtain some results on the convergence for the method of lines for FDE.