Coupling of microscopic and phase transition models at boundary

Mauro Garavello; Benedetto Piccoli

doi:10.3934/nhm.2013.8.649

Article Contents

2013, Volume 8, Issue 3: 649-661. Doi: 10.3934/nhm.2013.8.649

This issue Previous Article Existence of optima and equilibria for traffic flow on networks Next Article A dynamical two-dimensional traffic model in an anisotropic network

Coupling of microscopic and phase transition models at boundary

Mauro Garavello^1, and
Benedetto Piccoli^2,

1.
Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, via R. Cozzi 53 - Edificio U5, 20125 - Milano
2.
Joseph and Loretta Lopez Chair Professor of Mathematics, Department of Mathematical Sciences and Program Director, Center for Computational and Integrative Biology, Rutgers University - Camden, 311 N 5th Street, Camden, NJ 08102

Received: February 28, 2013

Revised: June 30, 2013

Published: August 2013

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Abstract

This paper deals with coupling conditions between the classical microscopic Follow The Leader model and a phase transition (PT) model. We propose a solution at the interface between the two models. We describe the solution to the Riemann problem.

Keywords:

Mathematics Subject Classification: Primary: 90B20; Secondary: 35L65.

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