Nonuniqueness of weak solutions to the dissipative Aw-Rascle model

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00587701" target="_blank" >RIV/67985840:_____/24:00587701 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00245-024-10158-x" target="_blank" >https://doi.org/10.1007/s00245-024-10158-x</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00245-024-10158-x" target="_blank" >10.1007/s00245-024-10158-x</a>

Result language
angličtina
Original language name
Nonuniqueness of weak solutions to the dissipative Aw-Rascle model
Original language description
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.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA21-02411S" target="_blank" >GA21-02411S: Solving ill posed problems in the dynamics of compressible fluids</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)