Hydrodynamic Limit with a Weierstrass-type result

TL;DR

This paper demonstrates that any positive, continuous, and bounded function can serve as the diffusion coefficient in a gradient interacting particle system, using a novel construction and entropy method.

Contribution

It introduces a method to realize arbitrary diffusion coefficients in particle systems, expanding the understanding of hydrodynamic limits.

Findings

Any positive, continuous, bounded function can be realized as a diffusion coefficient.

The construction relies on a specific model and entropy techniques.

The approach broadens the class of diffusion behaviors achievable in particle systems.

Abstract

We show that any positive, continuous, and bounded function can be realised as the diffusion coefficient of an evolution equation associated with a gradient interacting particle system. The proof relies on the construction of an appropriate model and on the entropy method.