Deterministic particle approximation of aggregation diffusion equations with nonlinear mobility
Analysis of PDEs
2022-09-23 v1
Abstract
We consider a class of aggregation-diffusion equations on unbounded one dimensional domains with Lipschitz nonincreasing mobility function. We show strong -convergence of a suitable deterministic particle approximation to weak solutions of a class aggregation-diffusion PDEs (coinciding with the classical ones in the no vacuum regions) for any bounded initial data of finite energy. In order to prove well-posedness and convergence of the scheme with no BV or no vacuum assumptions and overcome the issues posed in this setting by the presence of a mobility function, we improve and strengthen the techniques introduced in arXiv:2012.01966(2).
Cite
@article{arxiv.2209.10884,
title = {Deterministic particle approximation of aggregation diffusion equations with nonlinear mobility},
author = {Sara Daneri and Emanuela Radici and Eris Runa},
journal= {arXiv preprint arXiv:2209.10884},
year = {2022}
}
Comments
33 pages, 0 figures. arXiv admin note: text overlap with arXiv:2012.01966