Time-varying Riemann solvers for conservation laws on networks
type: Item
instance of: scholarly article
title: Time-varying Riemann solvers for conservation laws on networks
zbMATH Open document ID: 1166.90006
author: Mauro Garavello
author: B. Piccoli
published in: Journal of Differential Equations
publication date: 2009-06-18T00:00:00Z
review text: This paper deals with a scalar partial differential equation in conservation form on a network, composed by a finite collection of arcs connected together at nodes. To describe the dynamics, it is sufficient to define solutions to Riemann problems at nodes, which are Cauchy problems with constant initial conditions on the arcs meeting at the node. Using the same terminology of conservation laws on Euclidean spaces, the maps providing such solutions are called Riemann solvers at nodes. The authors prove existence of solutions to Cauchy problems on the whole network.
reviewed by: Nicolae Pop
Mathematics Subject Classification ID: 90B20
Mathematics Subject Classification ID: 35L65
zbMATH DE Number: 5566230
zbMATH Keywords: scalar conservation laws
zbMATH Keywords: traffic flow
zbMATH Keywords: Riemann solver
zbMATH Keywords: wave-front tracking
zbMATH Keywords: control problems
MaRDI profile type: Publication
full work available at URL: j.jde.2008.12.017
OpenAlex ID: W2007793424
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DOI: 10.1016/J.JDE.2008.12.017
description: scientific article; zbMATH DE number 5566230