Dirk Helbing

Alberto Bressan

Luigi Ambrosio

Axel Klar

Enrique Zuazua

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.

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

Modelling and Optimisation of Flows on Networks

Mark Williams

Denis Serre

Kevin Zumbrun

This volume includes four lecture courses by Bressan, Serre, Zumbrun and Williams and a Tutorial by Bressan on the Center Manifold Theorem. Bressan introduces the vanishing viscosity approach and clearly explains the building blocks of the theory. Serre focuses on existence and stability for discrete shock profiles. The lectures by Williams and Zumbrun deal with the stability of multidimensional fronts.

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 14-21, 2003

Hyperbolic Systems of Balance Laws

Alberto Bressan

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