| 561 | RWTH Publication No: 819798 2021 |
| TITLE | Stability analysis of a hyperbolic stochastic Galerkin formulation for the Aw-Rascle-Zhang model with relaxation |
| AUTHORS | Stephan Gerster, Michael Herty, Elisa Iacomini |
| ABSTRACT | We investigate the propagation of uncertainties in the Aw-Rascle-Zhang model, which belongs to a class of second order traffic flow models described by a system of nonlinear hyperbolic equations. The stochastic quantities are expanded in terms of wavelet-based series expansions. Then, they are projected to obtain a deterministic system for the coefficients in the truncated series. Stochastic Galerkin formulations are presented in conservative form and for smooth solutions also in the corresponding non-conservative form. This allows to obtain stabilization results, when the system is relaxed to a first-order model. Computational tests illustrate the theoretical results. |
| KEYWORDS | Traffic flow, uncertainty quantification, stability analysis, Aw-Rascle-Zhang model, stochastic Galerkin, Chapman-Enskog expansion |
| DOI | 10.3934/mbe.2021220 |
| PUBLICATION | Mathematical Biosciences and Engineering, 2021, Volume 18, Issue 4: 4372-4389 |
