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.
