Coupling of microscopic and phase transition models at boundary

Mauro Garavello; Benedetto Piccoli; Mauro Garavello; Benedetto Piccoli

doi:10.3934/nhm.2013.8.649

Networks and Heterogeneous Media

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

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Coupling of microscopic and phase transition models at boundary

Mauro Garavello ^{1
,},
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: 01 March 2013 Revised: 01 July 2013
Primary: 90B20; Secondary: 35L65.

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.
- Follow the Leader,
- phase transition model,
- conservation laws,
- coupling conditions,
- Cauchy Problem
Citation: Mauro Garavello, Benedetto Piccoli. Coupling of microscopic and phase transition models at boundary[J]. Networks and Heterogeneous Media, 2013, 8(3): 649-661. doi: 10.3934/nhm.2013.8.649

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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.

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