Nonlinear Fokker-Planck Flows and their Probabilistic Counterparts

2024
ISBN: 978-3-031-61733-1
Verlag: Springer Nature Switzerland

Buch, Englisch, 214 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 347 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Röckner, Michael

Barbu, Viorel

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

- 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.

Über Autor(innen)

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 Röckneris 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.