03295nam a22005535i 4500 978-3-031-61734-8 DE-He213 20251030112318.0 cr nn 008mamaa 240618s2024 sz | s |||| 0|eng d 9783031617348 978-3-031-61734-8 10.1007/978-3-031-61734-8 doi QC19.2-20.85 PHU bicssc SCI040000 bisacsh PHU thema Barbu, Viorel. author. aut http://id.loc.gov/vocabulary/relators/aut 78863 Nonlinear Fokker-Planck Flows and their Probabilistic Counterparts [electronic resource] / by Viorel Barbu, Michael Röckner. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. IX, 214 p. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Lecture Notes in Mathematics, 1617-9692 ; 2353 - 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. Mathematical physics. Differential equations. Stochastic analysis. 59375 Mathematical Physics. Differential Equations. Stochastic Analysis. 59375 Röckner, Michael. author. aut http://id.loc.gov/vocabulary/relators/aut 78864 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031617331 Printed edition: 9783031617355 Lecture Notes in Mathematics, 1617-9692 ; 2353 75434 https://doi.org/10.1007/978-3-031-61734-8 ZDB-2-SMA ZDB-2-SXMS ZDB-2-LNM 60807 60807