Zero-diffusion Limit for Aggregation Equations over Bounded Domains
Analysis of PDEs
2018-09-07 v1 Numerical Analysis
Probability
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.
Cite
@article{arxiv.1809.01763,
title = {Zero-diffusion Limit for Aggregation Equations over Bounded Domains},
author = {Razvan C. Fetecau and Hui Huang and Daniel Messenger and Weiran Sun},
journal= {arXiv preprint arXiv:1809.01763},
year = {2018}
}