Macroscopic Models for Vehicular Flows and Crowd Dynamics: Theory and Applications

Classical and Non–Classical Advanced Mathematics for Real Life Applications

Authors:

ISBN: 978-3-319-00154-8 (Print) 978-3-319-00155-5 (Online)

Table of contents (17 chapters)

  1. Front Matter

    Pages 1-10

  2. No Access

    Book Chapter

    Pages 1-7

    Introduction

  3. Part I-Mathematical Theory

    1. Front Matter

      Pages 9-9

    2. No Access

      Book Chapter

      Pages 11-21

      Mathematical Preliminaries

    3. No Access

      Book Chapter

      Pages 23-42

      One-Dimensional Scalar Conservation Laws

    4. No Access

      Book Chapter

      Pages 43-50

      The Riemann Problem

    5. No Access

      Book Chapter

      Pages 51-62

      The Cauchy Problem

    6. No Access

      Book Chapter

      Pages 63-91

      The Initial-Boundary Value Problem and the Constraint

    7. No Access

      Book Chapter

      Pages 93-110

      One-Dimensional Systems of Conservation Laws

    8. No Access

      Book Chapter

      Pages 111-120

      One-Dimensional Systems of Balance Laws (Weakly Coupled)

  4. Part II-Models for Vehicular Traffic

    1. Front Matter

      Pages 121-121

    2. No Access

      Book Chapter

      Pages 123-138

      Vehicular Traffic

    3. No Access

      Book Chapter

      Pages 139-148

      Equilibrium Traffic Models

    4. No Access

      Book Chapter

      Pages 149-160

      Generalizations of Equilibrium Traffic Models

    5. No Access

      Book Chapter

      Pages 161-166

      Cost Functionals

    6. No Access

      Book Chapter

      Pages 167-173

      Numerical Applications

    7. No Access

      Book Chapter

      Pages 175-190

      Non-equilibrium Traffic Models

  5. Part III-Models for Pedestrian Traffic

    1. Front Matter

      Pages 191-191

    2. No Access

      Book Chapter

      Pages 193-201

      General Concepts

    3. No Access

      Book Chapter

      Pages 203-226

      The CR Model

    4. No Access

      Book Chapter

      Pages 227-237

      Applications

  6. Back Matter

    Pages 239-242