03642nam 22006975 450 991086523770332120251217104230.09783031617348(electronic bk.)978303161733110.1007/978-3-031-61734-8(MiAaPQ)EBC31495521(Au-PeEL)EBL31495521(CKB)32315573600041(PPN)27980038X(DE-He213)978-3-031-61734-8(EXLCZ)993231557360004120240618d2024 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierNonlinear Fokker-Planck Flows and their Probabilistic Counterparts /by Viorel Barbu, Michael Röckner1st ed. 2024.Cham :Springer Nature Switzerland :Imprint: Springer,2024.1 online resource (219 pages)Lecture Notes in Mathematics,1617-9692 ;2353Print version: Barbu, Viorel Nonlinear Fokker-Planck Flows and Their Probabilistic Counterparts Cham : Springer,c2024 9783031617331 - 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.This 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.Lecture Notes in Mathematics,1617-9692 ;2353Mathematical physicsDifferential equationsStochastic analysisMathematical PhysicsDifferential EquationsStochastic AnalysisFísica matemàticathubEquacions diferencials no linealsthubAnàlisi estocàsticathubEquació de Fokker-PlanckthubLlibres electrònicsthubMathematical physics.Differential equations.Stochastic analysis.Mathematical Physics.Differential Equations.Stochastic Analysis.Física matemàticaEquacions diferencials no linealsAnàlisi estocàsticaEquació de Fokker-Planck530.15Barbu Viorel13745Röckner Michael59656MiAaPQMiAaPQMiAaPQ9910865237703321Nonlinear Fokker-Planck Flows and Their Probabilistic Counterparts4169383UNINA