Nečas Center Series

Dynamics and Analysis of Alignment Models of Collective Behavior

Authors: Shvydkoy, Roman

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  • Introduces a special class of alignment model called the Cucker-Smale system as well as its kinetic and hydrodynamic counterparts
  • Presents cutting-edge research in the area of collective behavior, including emerging techniques from fluid mechanics, fractional analysis, and kinetic theory
  • Features open problems throughout, motivating readers to pursue future research in this active area
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eBook 64,19 €
price for Spain (gross)
  • ISBN 978-3-030-68147-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 77,99 €
price for Spain (gross)
  • ISBN 978-3-030-68146-3
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this book

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.

About the authors

Roman Shvydkoy is Professor of Mathematics at the University of Illinois at Chicago and a recipient of a 2018 Simons Fellowship in Mathematics.

Table of contents (9 chapters)

Table of contents (9 chapters)

Buy this book

eBook 64,19 €
price for Spain (gross)
  • ISBN 978-3-030-68147-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 77,99 €
price for Spain (gross)
  • ISBN 978-3-030-68146-3
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Dynamics and Analysis of Alignment Models of Collective Behavior
Authors
Series Title
Nečas Center Series
Copyright
2021
Publisher
Birkhäuser Basel
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-68147-0
DOI
10.1007/978-3-030-68147-0
Softcover ISBN
978-3-030-68146-3
Series ISSN
2523-3343
Edition Number
1
Number of Pages
XIV, 208
Number of Illustrations
14 b/w illustrations, 2 illustrations in colour
Topics