03081nam a22005055i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001700172072001600189072002300205072001500228100008300243245013300326250001800459264006900477300003300546336002600579337002600605338003600631347002400667490005300691505026100744520101201005650002602017650002802043650003202071650002602103650002802129650003202157700008802189710003402277773002602311776003602337776003602373830006002409856004602469912001402515912001502529912001402544999001702558978-3-031-61734-8DE-He21320251030112318.0cr nn 008mamaa240618s2024    sz |    s    |||| 0|eng d  a97830316173489978-3-031-61734-87 a10.1007/978-3-031-61734-82doi 4aQC19.2-20.85 7aPHU2bicssc 7aSCI0400002bisacsh 7aPHU2thema1 aBarbu, Viorel.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut97886310aNonlinear Fokker-Planck Flows and their Probabilistic Counterpartsh[electronic resource] /cby Viorel Barbu, Michael Röckner.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aIX, 214 p.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aLecture Notes in Mathematics,x1617-9692 ;v23530 a- 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.  aThis 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. 0aMathematical physics. 0aDifferential equations. 0aStochastic analysis.95937514aMathematical Physics.24aDifferential Equations.24aStochastic Analysis.9593751 aRöckner, Michael.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut9788642 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303161733108iPrinted edition:z9783031617355 0aLecture Notes in Mathematics,x1617-9692 ;v235397543440uhttps://doi.org/10.1007/978-3-031-61734-8  aZDB-2-SMA  aZDB-2-SXMS  aZDB-2-LNM  c60807d60807