Nonlinear Fokker-Planck Flows and Their Probabilistic Counterparts

• Autore: Barbu Viorel
• Pubblicazione: Cham : , : Springer, , 2024; ©2024
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (219 pages)
• Altri autori: RöcknerMichael
• Nota di contenuto: Intro -- Preface -- Contents -- Symbols and Notation -- 1 Introduction -- 2 Existence of Nonlinear Fokker-Planck Flows -- 2.1 Existence for the NFPE (2.1) -- 2.2 Existence and Uniqueness of Mild Solutions to Isotropic NFPE -- 2.3 Uniqueness of Distributional Solutions to NFPE -- 2.4 NFPEs with Superlinear Diffusion -- 2.5 Smoothing Effect of NFP Flow on Initial Data -- 2.6 NFPE with a Measure as Initial Datum -- 2.7 NFPEs with Discontinuous Coefficients -- 2.8 NFPE with Fractional Laplacian -- 2.9 A Splitting Formula for NFPE -- Comments to Chap. 2 -- 3 Time Dependent Fokker-Planck Equations -- 3.1 Time Varying Fokker-Planck Flows -- 3.2 Fokker-Planck Periodic Flows -- Comments to Chap. 3 -- 4 Convergence to Equilibrium of Nonlinear Fokker-Planck Flows -- 4.1 The H-Theorem for the Nonlinear Fokker-Planck Equations -- 4.2 Attractors for Nonlinear Fokker-Planck Flows -- 4.3 The Ergodicity of Nonlinear Fokker-Planck Flows -- Comments to Chap. 4 -- 5 Markov Processes Associated with Nonlinear Fokker-Planck Equations -- 5.1 Fokker-Planck Equations and McKean-Vlasov SDEs -- 5.2 Uniqueness of Weak Solutions to McKean-Vlasov SDEs and Corresponding Nonlinear Markov Processes -- 5.3 Strong Solutions to McKean-Vlasov SDEs -- 6 Appendix -- 6.1 Nonlinear m-Accretive Operators -- 6.2 Semigroups of Contractions in Banach Spaces -- 6.3 Riesz Potentials -- References -- Index.
• Titolo autorizzato: Nonlinear Fokker-Planck Flows and Their Probabilistic Counterparts
• ISBN: 9783031617348; 9783031617331
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910865237703321
• Lo trovi qui: Univ. Federico II
• Serie: Lecture Notes in Mathematics Series