Nonlinear Fokker-Planck flows and their probabilistic counterparts / Viorel Barbu, Michael Röckner.

Format:

Book

Author/Creator:

Barbu, Viorel, Author.

Röckner, Michael, 1956- Author.

Series:

Lecture notes in mathematics (Springer-Verlag) ; 2353.

Lecture notes in mathematics ; 2353

Language:

English

Subjects (All):

Mathematical physics.

Differential equations.

Stochastic analysis.

Physical Description:

ix, 212 pages ; 24 cm.

Place of Publication:

Cham, Switzerland : Springer, [2024]

Summary:

"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."-- Back cover.

Contents:

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.

Notes:

Includes bibliographical references (pages 205-209) and index.

ISBN:

3031617339

9783031617331

OCLC:

1431180461