Macroscopic Models for Vehicular Flows and Crowd Dynamics: Theory and Applications: Classical and Non-Classical Advanced Mathematics for Real Life Applications (Understanding Complex Systems)

This monograph presents a systematic treatment of the theory for hyperbolic conservation laws and their applications to vehicular traffics and crowd dynamics. In the first part of the book, the author presents very basic considerations and gradually introduces the mathematical tools necessary to describe and understand the mathematical models developed in the following parts focusing on vehicular and pedestrian traffic. The book is a self-contained valuable resource for advanced courses in mathematical modeling, physics and civil engineering. A number of examples and figures facilitate a better understanding of the underlying concepts and motivations for the students. Important new techniques are presented, in particular the wave front tracking algorithm, the operator splitting approach, the non-classical theory of conservation laws and the constrained problems. This book is the first to present a comprehensive account of these fundamental new mathematical advances.