UID:
almahu_9949773127602882
Umfang:
IX, 214 p.
,
online resource.
Ausgabe:
1st ed. 2024.
ISBN:
9783031617348
Serie:
Lecture Notes in Mathematics, 2353
Inhalt:
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.
Anmerkung:
- 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.
In:
Springer Nature eBook
Weitere Ausg.:
Printed edition: ISBN 9783031617331
Weitere Ausg.:
Printed edition: ISBN 9783031617355
Sprache:
Englisch
DOI:
10.1007/978-3-031-61734-8
URL:
https://doi.org/10.1007/978-3-031-61734-8
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