Zero-diffusion Limit for Aggregation Equations over Bounded Domains
For mathematicians studying aggregation phenomena, this provides a sharper theoretical result with weaker assumptions, though it is an incremental improvement over existing methods.
The authors prove the zero-diffusion limit for aggregation equations on bounded convex domains, improving convergence rates and relaxing regularity assumptions compared to prior work. The derived rate matches numerical computations.
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.