Relaxation limit of the aggregation equation with pointy potential
Abstract
This work is devoted to the study of a relaxation limit of the so-called aggregation equation with a pointy potential in one dimensional space. The aggregation equation is by now widely used to model the dynamics of a density of individuals attracting each other through a potential. When this potential is pointy, solutions are known to blow up in final time. For this reason, measure-valued solutions have been defined. In this paper, we investigate an approximation of such measure-valued solutions thanks to a relaxation limit in the spirit of Jin and Xin. We study the convergence of this approximation and give a rigorous estimate of the speed of convergence in one dimension with the Newtonian potential. We also investigate the numerical discretization of this relaxation limit by uniformly accurate schemes.
Keywords
Cite
@article{arxiv.2105.13820,
title = {Relaxation limit of the aggregation equation with pointy potential},
author = {Benoît Fabrèges and Frédéric Lagoutière and Tran Tien and Nicolas Vauchelet},
journal= {arXiv preprint arXiv:2105.13820},
year = {2021}
}