English

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 L1L^1-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).

Keywords

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

R2 v1 2026-06-28T01:53:01.286Z