A fuzzy $q$-closest alignment model
Analysis of PDEs
2022-10-12 v1
Abstract
The paper examines the problems related to the well-posedness of the Cucker-Smale model with communication restricted to the -closest neighbors, known also as the Cucker-Dong model. With agents oscillating on the boundary of different clusters, the system becomes difficult to precisely define, which leads to further problems with kinetic limits as the number of agents tends to infinity. We introduce the fuzzy -closest system, which circumvents the issues with well-posedness. For such a system we prove a stability estimate for measure-valued solutions and perform the kinetic mean-field limit.
Cite
@article{arxiv.2210.05319,
title = {A fuzzy $q$-closest alignment model},
author = {Piotr B. Mucha and Jan Peszek},
journal= {arXiv preprint arXiv:2210.05319},
year = {2022}
}
Comments
17 pages