---

＜電子ブック＞
Nonlinear Fokker-Planck Flows and their Probabilistic Counterparts / by Viorel Barbu, Michael Röckner
(Lecture Notes in Mathematics. ISSN:16179692 ; 2353)

版	1st ed. 2024.
出版者	(Cham : Springer Nature Switzerland : Imprint: Springer)
出版年	2024
本文言語	英語
大きさ	IX, 214 p : online resource
著者標目	*Barbu, Viorel author Röckner, Michael author SpringerLink (Online service)
件　名	LCSH:Mathematical physics LCSH:Differential equations LCSH:Stochastic analysis FREE:Mathematical Physics FREE:Differential Equations FREE:Stochastic Analysis
一般注記	- 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 HTTP:URL=https://doi.org/10.1007/978-3-031-61734-8

 類似資料