© 2013

Modelling and Optimisation of Flows on Networks

Cetraro, Italy 2009, Editors: Benedetto Piccoli, Michel Rascle


Part of the Lecture Notes in Mathematics book series (LNM, volume 2062)

Also part of the C.I.M.E. Foundation Subseries book sub series (LNMCIME, volume 2062)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Luigi Ambrosio, Nicola Gigli
    Pages 1-155
  3. Dirk Helbing, Martin Treiber, Arne Kesting, Martin Schönhof
    Pages 303-333
  4. Dirk Helbing, Jan Siegmeier, Stefan Lämmer
    Pages 335-355
  5. Simone Göttlich, Axel Klar
    Pages 395-461
  6. Back Matter
    Pages 495-497

About this book


In recent years flows in networks have attracted the interest of many researchers from different areas, e.g. applied mathematicians, engineers, physicists, economists. The main reason for this ubiquity is the wide and diverse range of applications, such as vehicular traffic, supply chains, blood flow, irrigation channels, data networks and others.
This book presents an extensive set of notes by world leaders on the main mathematical techniques used to address such problems, together with investigations into specific applications. The main focus is on partial differential equations in networks, but ordinary differential equations and optimal transport are also included. Moreover, the modeling is completed by analysis, numerics, control and optimization of flows in networks.
The book will be a valuable resource for every researcher or student interested in the subject.


35R02, 35L65, 90B20 Optimal transport Partial differential equations Traffic flow Vehicular traffic

Authors and affiliations

  1. 1.Department of MathematicsScuola Normale SuperiorePisaItaly
  2. 2.State College, Dept. MathematicsPenn State UniversityUniversity ParkUSA
  3. 3.Chair of Sociology, in particular of Mod, CLU E 1ETH Zurich, Swiss Federal Institute of TZurichSwitzerland
  4. 4., Fachbereich MathematikTechnische Universität KaiserslauternKaiserslauternGermany
  5. 5., Depto. MatematicasBCAM – Basque Center for Applied MathemaBilbaoSpain

Bibliographic information

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