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Titlebook: Dynamics and Analysis of Alignment Models of Collective Behavior; Roman Shvydkoy Book 2021 Springer Nature Switzerland AG 2021 Cucker-Smal

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發(fā)表于 2025-3-21 18:00:14 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書(shū)目名稱Dynamics and Analysis of Alignment Models of Collective Behavior
編輯Roman Shvydkoy
視頻videohttp://file.papertrans.cn/284/283943/283943.mp4
概述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, inc
叢書(shū)名稱Ne?as Center Series
圖書(shū)封面Titlebook: Dynamics and Analysis of Alignment Models of Collective Behavior; Roman Shvydkoy Book 2021 Springer Nature Switzerland AG 2021 Cucker-Smal
描述.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...Dynam
出版日期Book 2021
關(guān)鍵詞Cucker-Smale System; Collective behavior models; Collective behavior flow; Alignment systems math; Kinet
版次1
doihttps://doi.org/10.1007/978-3-030-68147-0
isbn_softcover978-3-030-68146-3
isbn_ebook978-3-030-68147-0Series ISSN 2523-3343 Series E-ISSN 2523-3351
issn_series 2523-3343
copyrightSpringer Nature Switzerland AG 2021
The information of publication is updating

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Kinetic Models,esponding kinetic formulation and its variants can be derived formally via the BBGKY hierarchy. We will present a rigorous derivation of the Vlasov-type kinetic model via the mean-field limit and along the way establish contractivity and asymptotic stability estimates for solutions. Many of the coll
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Euler Alignment System,o the micro- and meso-systems, in the hydrodynamic context of the EAS with convolution-type communication. Further discussion will shift to local kernels demonstrating capabilities and limitations of the spectral method. This will motivate the introduction of the topological models later in the late
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Local Well-Posedness and Continuation Criteria,quation with a damping mechanism, while the latter is a degenerate fractional parabolic system with dissipation in the momentum equation. In this chapter we will go through the first routine but very much essential step—proving local existence of classical solutions and setting a convenient function
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Global Solutions to Multidimensional Systems, threshold condition is known, and in the singular case, the question is wide open. However, certain classes of special solutions do permit global existence. Those include solutions with small initial velocity fluctuations, small spectral gap of the symmetric velocity strain tensor, or special class
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https://doi.org/10.1007/978-3-030-68147-0Cucker-Smale System; Collective behavior models; Collective behavior flow; Alignment systems math; Kinet
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