The Cauchy problem at a node with buffer

Mauro Garavello; Paola Goatin

doi:10.3934/dcds.2012.32.1915

Article Contents

2012, Volume 32, Issue 6: 1915-1938. Doi: 10.3934/dcds.2012.32.1915

This issue Previous Article Next Article Analysis of a Burgers equation with singular resonant source term and convergence of well-balanced schemes

The Cauchy problem at a node with buffer

Mauro Garavello^1, and
Paola Goatin^2,

1.
Dipartimento di Scienze e Tecnologie Avanzate, Università del Piemonte Orientale “A. Avogadro”, viale T. Michel 11, 15121 Alessandria
2.
INRIA Sophia Antipolis - Méditerranée, EPI OPALE, 2004, route des Lucioles - BP 93, 06902 Sophia Antipolis Cedex

Received: December 31, 2010

Revised: September 30, 2011

Published: May 2012

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Abstract

We consider the Lighthill-Whitham-Richards traffic flow model on a network composed by an arbitrary number of incoming and outgoing arcs connected together by a node with a buffer. Similar to [15], we define the solution to the Riemann problem at the node and we prove existence and well posedness of solutions to the Cauchy problem, by using the wave-front tracking technique and the generalized tangent vectors.

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Mathematics Subject Classification: Primary: 36L65; Secondary: 90B20.

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References

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