English

Hard-congestion limit of the p-system in the BV setting

Analysis of PDEs 2022-11-17 v1

Abstract

This note is concerned with the rigorous justification of the so-called hard congestion limit from a compressible system with singular pressure towards a mixed compressible-incompressible system modeling partially congested dynamics, for small data in the framework of BV solutions. We present a first convergence result for perturbations of a reference state represented by a single propagating large interface front, while the study of a more general framework where the reference state is constituted by multiple interface fronts is announced in the conclusion and will be the subject of a forthcoming paper. A key element of the proof is the use of a suitably weighted Glimm functional that allows to obtain precise estimates on the BV norm of the front-tracking approximation.

Keywords

Cite

@article{arxiv.2211.08767,
  title  = {Hard-congestion limit of the p-system in the BV setting},
  author = {Fabio Ancona and Roberta Bianchini and Charlotte Perrin},
  journal= {arXiv preprint arXiv:2211.08767},
  year   = {2022}
}