Geodesic
Hard-congestion limit of the p-system in the BV setting
Fabio Ancona1 ; Roberta Bianchini2 ; Charlotte Perrin3
1Dipartimento di Matematica "Tullio Levi-Civita", Universitàdi Padova, Italy
2Consiglio Nazionale delle Ricerche, Istituto per le Applicazioni del Calcolo, 00185 Rome, Italy
3CNRS, Aix Marseille Univ., I2M, Marseille, France
ESAIM. Proceedings, Tome 72 (2023), pp. 41-63

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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.
DOI : 10.1051/proc/202372041

Fabio Ancona  1   ; Roberta Bianchini  2   ; Charlotte Perrin  3

1 Dipartimento di Matematica "Tullio Levi-Civita", Universitàdi Padova, Italy
2 Consiglio Nazionale delle Ricerche, Istituto per le Applicazioni del Calcolo, 00185 Rome, Italy
3 CNRS, Aix Marseille Univ., I2M, Marseille, France 
Fabio Ancona; Roberta Bianchini; Charlotte Perrin. Hard-congestion limit of the p-system in the BV setting. ESAIM. Proceedings, Tome 72 (2023), pp. 41-63. doi: 10.1051/proc/202372041
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