Zero-diffusion Limit for Aggregation Equations over Bounded Domains

TL;DR

This paper proves the zero-diffusion limit for aggregation models in bounded domains, using a novel coupling method that relaxes regularity assumptions and aligns with numerical results.

Contribution

It introduces a new approach based on coupling PDEs with SDEs, improving convergence rates and relaxing regularity conditions compared to previous work.

Findings

Established zero-diffusion limit for continuous and discrete models

Improved convergence rate in terms of diffusion coefficient

Validated results with numerical computations

Abstract

We establish the zero-diffusion limit for both continuous and discrete aggregation models over convex and bounded domains. Compared with a similar zero-diffusion limit derived in [44], our approach is different and relies on a coupling method connecting PDEs with their underlying SDEs. Moreover, our result relaxes the regularity assumptions on the interaction and external potentials and improves the convergence rate (in terms of the diffusion coefficient). The particular rate we derive is shown to be consistent with numerical computations.