LEADER 03642nam 22006975 450 001 9910865237703321 005 20251217104230.0 010 $a9783031617348$b(electronic bk.) 010 $z9783031617331 024 7 $a10.1007/978-3-031-61734-8 035 $a(MiAaPQ)EBC31495521 035 $a(Au-PeEL)EBL31495521 035 $a(CKB)32315573600041 035 $a(PPN)27980038X 035 $a(DE-He213)978-3-031-61734-8 035 $a(EXLCZ)9932315573600041 100 $a20240618d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aNonlinear Fokker-Planck Flows and their Probabilistic Counterparts /$fby Viorel Barbu, Michael Röckner 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (219 pages) 225 1 $aLecture Notes in Mathematics,$x1617-9692 ;$v2353 311 08$aPrint version: Barbu, Viorel Nonlinear Fokker-Planck Flows and Their Probabilistic Counterparts Cham : Springer,c2024 9783031617331 327 $a- Introduction -- Existence of nonlinear Fokker?Planck flows -- Time dependent Fokker?Planck equations -- Convergence to equilibrium of nonlinear Fokker?Planck flows -- Markov processes associated with nonlinear Fokker?Planck equations -- Appendix. 330 $aThis book delves into a rigorous mathematical exploration of the well-posedness and long-time behavior of weak solutions to nonlinear Fokker-Planck equations, along with their implications in the theory of probabilistically weak solutions to McKean-Vlasov stochastic differential equations and the corresponding nonlinear Markov processes. These are widely acknowledged as essential tools for describing the dynamics of complex systems in disordered media, as well as mean-field models. The resulting stochastic processes elucidate the microscopic dynamics underlying the nonlinear Fokker-Planck equations, whereas the solutions of the latter describe the evolving macroscopic probability distributions. The intended audience for this book primarily comprises specialists in mathematical physics, probability theory and PDEs. It can also be utilized as a one-semester graduate course for mathematicians. Prerequisites for the readers include a solid foundation in functional analysis and probability theory. 410 0$aLecture Notes in Mathematics,$x1617-9692 ;$v2353 606 $aMathematical physics 606 $aDifferential equations 606 $aStochastic analysis 606 $aMathematical Physics 606 $aDifferential Equations 606 $aStochastic Analysis 606 $aFísica matemàtica$2thub 606 $aEquacions diferencials no lineals$2thub 606 $aAnàlisi estocàstica$2thub 606 $aEquació de Fokker-Planck$2thub 608 $aLlibres electrònics$2thub 615 0$aMathematical physics. 615 0$aDifferential equations. 615 0$aStochastic analysis. 615 14$aMathematical Physics. 615 24$aDifferential Equations. 615 24$aStochastic Analysis. 615 7$aFísica matemàtica 615 7$aEquacions diferencials no lineals 615 7$aAnàlisi estocàstica 615 7$aEquació de Fokker-Planck 676 $a530.15 700 $aBarbu$b Viorel$013745 701 $aRöckner$b Michael$059656 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910865237703321 996 $aNonlinear Fokker-Planck Flows and Their Probabilistic Counterparts$94169383 997 $aUNINA