0587701 - MÚ 2025 RIV DE eng J - Journal Article
Chaudhuri, N. - Feireisl, Eduard - Zatorska, E.
Nonuniqueness of weak solutions to the dissipative Aw-Rascle model.
Applied Mathematics and Optimization. Roč. 90, č. 1 (2024), č. článku 19. ISSN 0095-4616. E-ISSN 1432-0606
R&D Projects: GA ČR(CZ) GA21-02411S
Institutional support: RVO:67985840
Keywords : convex-integration * dissipative Aw-Rascle system * weak solutions
OECD category: Pure mathematics
Impact factor: 1.8, year: 2022
Method of publishing: Open access
https://doi.org/10.1007/s00245-024-10158-x

We prove nonuniqueness of weak solutions to multi-dimensional generalisation of the Aw-Rascle model of vehicular traffic. Our generalisation includes the velocity offset in a form of gradient of density function, which results in a dissipation effect, similar to viscous dissipation in the compressible viscous fluid models. We show that despite this dissipation, the extension of the method of convex integration can be applied to generate infinitely many weak solutions connecting arbitrary initial and final states. We also show that for certain choice of data, ill posedness holds in the class of admissible weak solutions.
Permanent Link: https://hdl.handle.net/11104/0354794