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

Fabio Ancona; Roberta Bianchini; Charlotte Perrin

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arXiv · 2211.08767

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

Fabio Ancona·Roberta Bianchini·Charlotte Perrin

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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.

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Fabio Ancona, Roberta Bianchini, Charlotte Perrin. 2022-11-16. Hard-congestion limit of the p-system in the BV setting. https://arxiv.org/abs/2211.08767

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