Lack of BV bounds for approximate solutions to a two-phase transition model arising from vehicular traffic

Mohamed Benyahia (1) , Massimiliano D. Rosini (2)

1 GSSI - Gran Sasso Science Institute
2 UniFE - Università degli Studi di Ferrara = University of Ferrara

We consider wave-front tracking approximate solutions to a two-phase transition model for vehicular traffic. We construct an explicit example showing that the total variation in space of the solution blows up in finite time even for an initial datum with bounded total variation.

Mots clés: Conservation laws; phase transitions; Lighthill-Whitham-Richards model; Aw-Rascle-Zhang model; point constraint on the density flux; wave-front tracking; blow up in finite time

Domaines: Equations aux dérivées partielles [math.AP]

Mohamed Benyahia, Massimiliano D. Rosini. Lack of BV bounds for approximate solutions to a two-phase transition model arising from vehicular traffic. 2019. ⟨hal-02306582⟩