학술논문
Vanishing viscosity for a $2\times 2$ system modeling congested vehicular traffic.
Document Type
Journal
Author
Coclite, Giuseppe Maria (I-PBAR-MMM) AMS Author Profile; De Nitti, Nicola (D-ERL-DSC) AMS Author Profile; Garavello, Mauro (I-MILB-AM) AMS Author Profile; Marcellini, Francesca (I-BRSC-IFE) AMS Author Profile
Source
Subject
90 Operations research, mathematical programming -- 90B Operations research and management science
90B20Traffic problems
90B20
Language
English
Abstract
Summary: ``We prove the convergence of the vanishing viscosity approximation for a class of $2\times2$ systems of conservation laws, which includes a model of traffic flow in congested regimes. The structure of the system allows us to avoid the typical constraints on the total variation and the $L^1$ norm of the initial data. The key tool is the compensated compactness technique, introduced by Murat and Tartar, used here in the framework developed by Panov. The structure of the Riemann invariants is used to obtain the compactness estimates.''