0587701 - MÚ 2025 RIV DE eng J - Článek v odborném periodiku
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
Grant CEP: GA ČR(CZ) GA21-02411S
Institucionální podpora: RVO:67985840
Klíčová slova: convex-integration * dissipative Aw-Rascle system * weak solutions
Obor OECD: Pure mathematics
Impakt faktor: 1.8, rok: 2022
Způsob publikování: 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.
Trvalý link: https://hdl.handle.net/11104/0354794