Control problems for conservation laws with traffic applications. Modeling, analysis, and numerical methods
type: Item
instance of: scholarly article
title: Control problems for conservation laws with traffic applications. Modeling, analysis, and numerical methods
zbMATH Open document ID: 1501.35001
DOI: 10.1007/978-3-030-93015-8
author: Alexandre Bayen
author: Maria Laura Delle Monache
author: Mauro Garavello
author: Paola Goatin
author: B. Piccoli
published in: Progress in Nonlinear Differential Equations and Their Applications
publication date: 2022-02-07T00:00:00Z
review text: Conservation and balance laws on networks have been the subject of much research interest given their wide range of applications to real-world processes, particularly traffic flow. This open access monograph is the first to investigate different types of control problems for conservation laws that arise in the modeling of vehicular traffic. Four types of control problems are discussed -- boundary, decentralized, distributed, and Lagrangian control -- corresponding to, respectively, entrance points and tolls, traffic signals at junctions, variable speed limits, and the use of autonomy and communication. Because conservation laws are strictly connected to Hamilton-Jacobi equations, control of the latter is also considered. An appendix, reviewing the general theory of initial-boundary value problems for balance laws is included, as well as an appendix illustrating the main concepts in the theory of conservation laws on networks.
Mathematics Subject Classification ID: 35-02
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 76A30
Mathematics Subject Classification ID: 90B20
Mathematics Subject Classification ID: 93-02
zbMATH DE Number: 7470445
zbMATH Keywords: traffic flow
zbMATH Keywords: vehicular traffic
zbMATH Keywords: control problems
zbMATH Keywords: conservation laws
zbMATH Keywords: Hamilton-Jacobi equations
zbMATH Keywords: networks
reviewed by: Massimiliano D. Rosini
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-030-93015-8
OpenAlex ID: W4226441884
description: scientific article; zbMATH DE number 7470445