Overview
- Can be used as a one semester graduate course for mathematicians
- Devoted to existence and uniqueness of weak solutions to nonlinear Fokker-Planck equations
- Presents recent research material on nonlinear Fokker-Planck equations
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2353)
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About this book
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.
Keywords
Table of contents (6 chapters)
Authors and Affiliations
About the authors
Viorel Barbu is professor of Mathematics at Alexandru Ioan Cuza University (Romania) and also member of Romanian Academy and of European Academy of Science. He has published several monographs and textbooks on nonlinear analysis, infinite dimensional optimization, partial differential equations and Navier-Stokes equations with Springer, Academic Press, Kluwer, Birkhauser.
Michael Röckner is professor of Mathematics at Bielefeld University (Germany) and a distinguished visiting professor at CAS. He is a member of the Academia Europaea, the Academy of Sciences and Literature, Mainz, and a foreign honorary member of the Romanian Academy. His main areas of research are stochastic analysis, in particular, stochastic partial differential equations, the theory of Dirichlet forms and potential theory. He is a coauthor of several monographs in these fields.
Bibliographic Information
Book Title: Nonlinear Fokker-Planck Flows and their Probabilistic Counterparts
Authors: Viorel Barbu, Michael Röckner
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-031-61734-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2024
Softcover ISBN: 978-3-031-61733-1Published: 18 June 2024
eBook ISBN: 978-3-031-61734-8Published: 17 June 2024
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: IX, 214
Topics: Mathematical Physics, Analysis, Probability Theory and Stochastic Processes