1st Edition
Pedestrian Dynamics Mathematical Theory and Evacuation Control
Introduction
Motivation
Literature Survey
Outline
Derivation of Conservation Laws
Mass Conservation
Momentum Conservation
Energy Conservation
Combined Equations
General ConservationTraffic Models: One Dimensional Case
Lighthill-Whitham-Richards Model
Payne-Whitham Model
Aw-Rascle Model
Zhang Model
Pedestrian and Control Models in One Dimension
Traffic Models: Two-Dimensional Case
Two-Dimensional LWR Model
Two-Dimensional Payne-Whitham Model
Two-Dimensional Aw-Rascle Model
Two-Dimensional Zhang Model
Conservation Law Solutions
Method of Characteristics
Classical or Strong Solutions
Weak Solutions
Scalar Riemann Problem
Admissibility Conditions
Kruzkov’s Entropy Function
Well-posedness
Oleinik Entropy Condition
Scalar Initial-Boundary Problem
Traffic Control
Scalar Conservation Law Solution
Dynamical Systems and C0-Semigroups
Optimal Control
Optimal Flux Control for Scalar Conservation Law
Feedback Control for Scalar Law
Advective Feedback Control for Relaxation Systems
Wellposedness for Bounded Advection Control
Simulations for Advective Control
Godunov’s Method
Simulation Results for Advective Control
Conclusions
Summary
Contributions
Future Work
Biography
Pushkin Kachroo
