LEADER 03382nam 2200541 450 001 9910483133803321 005 20230421111730.0 010 $a3-030-68147-5 024 7 $a10.1007/978-3-030-68147-0 035 $a(CKB)4100000011934735 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 $a20220122d2021 uy 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 /$fRoman Shvydkoy 205 $a1st ed. 2021. 210 1$aCham, Switzerland :$cBirkha?user,$d[2021] 210 4$dŠ2021 215 $a1 online resource (XIV, 208 p. 16 illus., 2 illus. in color.) 225 1 $aNe?as Center Series,$x2523-3343 311 $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,$x2523-3343 606 $aMathematical models 606 $aModels matemātics$2thub 606 $aEquacions en derivades parcials$2thub 608 $aLlibres electrōnics$2thub 615 0$aMathematical models. 615 7$aModels matemātics 615 7$aEquacions en derivades parcials 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 LEADER 01167nam a2200277 i 4500 001 991001280159707536 008 051027s2005 nyub b 001 0 eng d 020 $a0415972175 035 $ab13348449-39ule_inst 040 $aDip.to Studi Giuridici$bita 082 0 $a932.022$222 100 1 $aCapponi, Livia,$d1975-$0622848 245 10$aAugustan Egypt :$bthe creation of a Roman province /$cLivia Capponi 260 $aNew York :$bRoutledge,$c2005 300 $axiii, 308 p. :$b1 map ;$c24 cm 440 0$aStudies in classics ;$v13 504 $aInclude riferimenti bibliografici (p. 187-281) e indici 600 04$aAugustus,$cImperatore di Roma,$d63 a.C.-14 d.C. 651 4$aEgitto$xStoria$yPeriodo Greco-Romano, 332 a.C.-640 d.C. 907 $a.b13348449$b18-12-07$c27-10-05 912 $a991001280159707536 945 $aLE027 R-III/E 12$g1$i2027000109876$lle027$o-$pE70.00$q-$rl$s- $t0$u0$v0$w0$x0$y.i14141358$z27-10-05 945 $aLE027 R-III/E 12$cC. 2$g1$i2027000139521$lle027$o-$pE88.38$q-$rl$s- $t0$u0$v0$w0$x0$y.i14635537$z18-12-07 996 $aAugustan Egypt$91093270 997 $aUNISALENTO 998 $ale027$b27-10-05$cm$da $e-$feng$gnyu$h0$i0