1.

Record Nr.

UNINA9910865237703321

Autore

Barbu Viorel

Titolo

Nonlinear Fokker-Planck Flows and their Probabilistic Counterparts / / by Viorel Barbu, Michael Röckner

Pubbl/distr/stampa

Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2024

ISBN

9783031617348

9783031617331

Edizione

[1st ed. 2024.]

Descrizione fisica

1 online resource (219 pages)

Collana

Lecture Notes in Mathematics, , 1617-9692 ; ; 2353

Altri autori (Persone)

RöcknerMichael

Disciplina

530.15

Soggetti

Mathematical physics

Differential equations

Stochastic analysis

Mathematical Physics

Differential Equations

Stochastic Analysis

Física matemàtica

Equacions diferencials no lineals

Anàlisi estocàstica

Equació de Fokker-Planck

Llibres electrònics

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di contenuto

- 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.

Sommario/riassunto

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.