Well-posedness results for the Generalized Aw-Rascle-Zhang model
Elio Marconi, Laura V. Spinolo
TL;DR
This paper proves existence, uniqueness, and stability for the Generalized Aw-Rascle-Zhang traffic model, providing rigorous mathematical foundations for this second order model used in traffic flow analysis.
Contribution
It offers the first comprehensive well-posedness analysis for the Generalized Aw-Rascle-Zhang model, extending previous work and ensuring its mathematical robustness.
Findings
Existence of solutions established
Uniqueness of solutions proven
Stability under certain conditions demonstrated
Abstract
We establish existence, uniqueness and stability results for the so-called Generalized Aw-Rascle-Zhang model, a second order traffic model introduced by Fan, Herty and Seibold. Our analysis is motivated by the companion paper 'Nonlocal Generalized Aw-Rascle-Zhang model: well-posedness and singular limit'.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Nonlinear Partial Differential Equations