Conservation laws on complex networks

Mauro Garavello; Benedetto Piccoli

doi:10.1016/j.anihpc.2009.04.001

Conservation laws on complex networks

Mauro Garavello, Benedetto Piccoli

Research output: Contribution to journal › Article › peer-review

47 Scopus citations

Abstract

This paper considers a system described by a conservation law on a general network and deals with solutions to Cauchy problems. The main application is to vehicular traffic, for which we refer to the Lighthill-Whitham-Richards (LWR) model. Assuming to have bounds on the conserved quantity, we are able to prove existence of solutions to Cauchy problems for every initial datum in L_loc¹. Moreover Lipschitz continuous dependence of the solution with respect to initial data is discussed.

Original language	English (US)
Pages (from-to)	1925-1951
Number of pages	27
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	26
Issue number	5
DOIs	https://doi.org/10.1016/j.anihpc.2009.04.001
State	Published - 2009
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Mathematical Physics
Applied Mathematics

Keywords

Networks
Scalar conservation laws
Traffic flow
Wave-front tracking

Access to Document

10.1016/j.anihpc.2009.04.001

Cite this

@article{dc2f003be02e4723b1836d1cfbca62b4,

title = "Conservation laws on complex networks",

abstract = "This paper considers a system described by a conservation law on a general network and deals with solutions to Cauchy problems. The main application is to vehicular traffic, for which we refer to the Lighthill-Whitham-Richards (LWR) model. Assuming to have bounds on the conserved quantity, we are able to prove existence of solutions to Cauchy problems for every initial datum in Lloc1. Moreover Lipschitz continuous dependence of the solution with respect to initial data is discussed.",

keywords = "Networks, Scalar conservation laws, Traffic flow, Wave-front tracking",

author = "Mauro Garavello and Benedetto Piccoli",

note = "Funding Information: * Corresponding author. E-mail addresses: mauro.garavello@mfn.unipmn.it (M. Garavello), piccoli@iac.rm.cnr.it (B. Piccoli). 1 Partially supported by Department of Mathematics and Applications, University of Milano-Bicocca.",

year = "2009",

doi = "10.1016/j.anihpc.2009.04.001",

language = "English (US)",

volume = "26",

pages = "1925--1951",

journal = "Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis",

issn = "0294-1449",

publisher = "Elsevier Masson SAS",

number = "5",

}

TY - JOUR

T1 - Conservation laws on complex networks

AU - Garavello, Mauro

AU - Piccoli, Benedetto

N1 - Funding Information: * Corresponding author. E-mail addresses: mauro.garavello@mfn.unipmn.it (M. Garavello), piccoli@iac.rm.cnr.it (B. Piccoli). 1 Partially supported by Department of Mathematics and Applications, University of Milano-Bicocca.

PY - 2009

Y1 - 2009

N2 - This paper considers a system described by a conservation law on a general network and deals with solutions to Cauchy problems. The main application is to vehicular traffic, for which we refer to the Lighthill-Whitham-Richards (LWR) model. Assuming to have bounds on the conserved quantity, we are able to prove existence of solutions to Cauchy problems for every initial datum in Lloc1. Moreover Lipschitz continuous dependence of the solution with respect to initial data is discussed.

AB - This paper considers a system described by a conservation law on a general network and deals with solutions to Cauchy problems. The main application is to vehicular traffic, for which we refer to the Lighthill-Whitham-Richards (LWR) model. Assuming to have bounds on the conserved quantity, we are able to prove existence of solutions to Cauchy problems for every initial datum in Lloc1. Moreover Lipschitz continuous dependence of the solution with respect to initial data is discussed.

KW - Networks

KW - Scalar conservation laws

KW - Traffic flow

KW - Wave-front tracking

UR - http://www.scopus.com/inward/record.url?scp=69749102653&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=69749102653&partnerID=8YFLogxK

U2 - 10.1016/j.anihpc.2009.04.001

DO - 10.1016/j.anihpc.2009.04.001

M3 - Article

AN - SCOPUS:69749102653

SN - 0294-1449

VL - 26

SP - 1925

EP - 1951

JO - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis

JF - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis

IS - 5

ER -

Conservation laws on complex networks

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this