Dynamics and analysis of alignment models of collective behavior / Roman Shvydkoy.
2021
QA401
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Details
Title
Dynamics and analysis of alignment models of collective behavior / Roman Shvydkoy.
Author
Shvydkoy, Roman, author.
ISBN
9783030681470 (electronic bk.)
3030681475 (electronic bk.)
3030681467 (print)
9783030681463 (print)
3030681475 (electronic bk.)
3030681467 (print)
9783030681463 (print)
Publication Details
Cham : Birkhäuser, 2021.
Language
English
Description
1 online resource (xiv, 208 pages)
Item Number
10.1007/978-3-030-68147-0 doi
Call Number
QA401
Dewey Decimal Classification
511/.8
Summary
This book introduces a class of alignment models based on the so-called Cucker-Smale system as well as its kinetic and hydrodynamic counterparts. Cutting edge research in the area of collective behavior is presented, including emerging techniques from fluid mechanics, fractional analysis, and kinetic theory. Analytical aspects are highlighted throughout, such as regularity theory and long time behavior of solutions. Featuring open problems, readers will be motivated to apply these breakthrough methods to future research. The chapters offer an overview of state of the art research with introductions to core concepts. Chapter One introduces the central focus of the book: The agent-based Cucker-Smale system. Further agent-based systems and alignment systems are covered in chapters Two and Three. Following this are chapters covering the kinetic and hydrodynamic variants of the Cucker-Smale system. The core well-posedness theory of both smooth and singular models is then presented. Chapter Eight discusses the fully developed one-dimensional theory. The final chapter presents some of the known partial results concerning the regularity of multidimensional Euler Alignment systems. Dynamics and Analysis of Alignment Models of Collective Behavior is ideal for graduate students and researchers studying PDEs, especially those interested in the active areas of collective behavior and alignment models.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Digital File Characteristics
text file
PDF
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed May 25, 2021).
Series
Nečas Center Series, 2523-3343
Available in Other Form
Print version: 9783030681463
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Online Access
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Table of Contents
Emergent phenomena and overview of existing models
Agent-based alignment systems
Forced systems
Kinetic models
Macroscopic description. Hydrodynamic limit
Euler Alignment System
Local well-posedness and continuation criteria
One-dimensional theory
Global solutions to multi-dimensional systems.
Agent-based alignment systems
Forced systems
Kinetic models
Macroscopic description. Hydrodynamic limit
Euler Alignment System
Local well-posedness and continuation criteria
One-dimensional theory
Global solutions to multi-dimensional systems.