Hydrodynamic limit for a zero-range process in the Sierpinski gasket

TL;DR

This paper establishes that the large-scale behavior of a zero-range process on graphs approximating the Sierpinski gasket converges to a nonlinear heat equation, with proofs of existence and uniqueness via finite-difference schemes.

Contribution

It introduces the hydrodynamic limit for zero-range processes on fractal graphs and proves the associated nonlinear heat equation's well-posedness.

Findings

Hydrodynamic limit is a nonlinear heat equation.

Existence and uniqueness of the hydrodynamic equation.

Application to graphs approximating the Sierpinski gasket.

Abstract

We prove that the hydrodynamic limit of a zero-range process evolving in graphs approximating the Sierpinski gasket is given by a nonlinear heat equation. We also prove existence and uniqueness of the hydrodynamic equation by considering a finite-difference scheme.