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010   $a3-030-68147-5
024 7 $a10.1007/978-3-030-68147-0
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035   $a(DE-He213)978-3-030-68147-0
035   $a(MiAaPQ)EBC6621463
035   $a(Au-PeEL)EBL6621463
035   $a(OCoLC)1256237371
035   $a(PPN)255885385
035   $a(EXLCZ)994100000011934735
100   $a20210513d2021      u|         0
101 0 $aeng
135   $aurnn#008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aDynamics and Analysis of Alignment Models of Collective Behavior /$fby Roman Shvydkoy
205   $a1st ed. 2021.
210  1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2021.
215   $a1 online resource (XIV, 208 p. 16 illus., 2 illus. in color.)
225 1 $aNe?as Center Series,$x2523-3351
311 08$a3-030-68146-7 
327   $aEmergent 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.
330   $aThis book introduces a class of alignment models based on the so-called Cucker-Smale system as well as its kinetic and hydrodynamic counterparts. Cutting edge research in the area of collective behavior is presented, including emerging techniques from fluid mechanics, fractional analysis, and kinetic theory. Analytical aspects are highlighted throughout, such as regularity theory and long time behavior of solutions. Featuring open problems, readers will be motivated to apply these breakthrough methods to future research. The chapters offer an overview of state of the art research with introductions to core concepts. Chapter One introduces the central focus of the book: The agent-based Cucker-Smale system. Further agent-based systems and alignment systems are covered in chapters Two and Three. Following this are chapters covering the kinetic and hydrodynamic variants of the Cucker-Smale system. The core well-posedness theory of both smooth and singular models is then presented. Chapter Eight discusses the fully developed one-dimensional theory. The final chapter presents some of the known partial results concerning the regularity of multidimensional Euler Alignment systems. Dynamics and Analysis of Alignment Models of Collective Behavior is ideal for graduate students and researchers studying PDEs, especially those interested in the active areas of collective behavior and alignment models.
410  0$aNe?as Center Series,$x2523-3351
606   $aMathematical models
606   $aBiomathematics
606   $aMathematical analysis
606   $aMathematical Modeling and Industrial Mathematics
606   $aMathematical and Computational Biology
606   $aAnalysis
615  0$aMathematical models.
615  0$aBiomathematics.
615  0$aMathematical analysis.
615 14$aMathematical Modeling and Industrial Mathematics.
615 24$aMathematical and Computational Biology.
615 24$aAnalysis.
676   $a511.8
700   $aShvydkoy$b Roman$0852938
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910483133803321
996   $aDynamics and Analysis of Alignment Models of Collective Behavior$91904773
997   $aUNINA