Roman Shvydkoy
Dynamics and Analysis of Alignment Models of Collective Behavior
Dynamics and Analysis of Alignment Models of Collective Behavior
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Excellent- More about Dynamics and Analysis of Alignment Models of Collective Behavior
This book introduces a class of alignment models based on the Cucker-Smale system and its kinetic and hydrodynamic counterparts, presenting cutting-edge research in collective behavior. It highlights analytical aspects such as regularity theory and long-time behavior of solutions and includes open problems for readers to apply these methods to future research.
Format: Paperback / softback
Length: 208 pages
Publication date: 14 May 2021
Publisher: Springer Nature Switzerland AG
This comprehensive book delves into the realm of alignment models, drawing inspiration from the Cucker-Smale system and its kinetic and hydrodynamic counterparts. It presents cutting-edge research in the field of collective behavior, encompassing emerging techniques from fluid mechanics, fractional analysis, and kinetic theory. Throughout, analytical aspects such as regularity theory and long-time behavior of solutions are emphasized. The book features open problems, encouraging readers to apply these breakthrough methods to future research endeavors.
The chapters provide an insightful overview of state-of-the-art research, introducing core concepts. Chapter One introduces the agent-based Cucker-Smale system, serving as the central focus of the book. Chapters Two and Three explore further agent-based systems and alignment systems. Subsequently, chapters delve into the kinetic and hydrodynamic variants of the Cucker-Smale system. The core well-posedness theory of both smooth and singular models is presented in Chapter Seven. Chapter Eight discusses the fully developed one-dimensional theory, while Chapter Nine presents some known partial results concerning the regularity of multidimensional Euler Alignment systems.
Dynamics and Analysis of Alignment Models of Collective Behavior is a valuable resource for graduate students and researchers specializing in Partial Differential Equations (PDEs), particularly those with interests in the active areas of collective behavior and alignment models. Its comprehensive coverage, analytical insights, and open problems make it an essential tool for advancing knowledge in this field.
Weight: 454g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030681463
Edition number: 1st ed. 2021
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