ZERO-DIFFUSION LIMIT FOR AGGREGATION EQUATIONS OVER BOUNDED DOMAINS

We investigate the zero-diffusion limit for both continuous and discrete aggregation-diffusion models over convex and bounded domains. Our approach relies on a coupling method connecting PDEs with their underlying SDEs. Compared with existing work, 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.

Automated summary

We investigate the zero-diffusion limit for both continuous and discrete aggregation-diffusion models over convex and bounded domains. Our result relaxes the regularity assumptions on the interaction and external potentials and improves the convergence rate.