03806nam 2200601 450 99646647440331620220906120228.03-540-46636-310.1007/BFb0086457(CKB)1000000000437102(SSID)ssj0000324683(PQKBManifestationID)12117818(PQKBTitleCode)TC0000324683(PQKBWorkID)10320413(PQKB)10312042(DE-He213)978-3-540-46636-9(MiAaPQ)EBC5594480(Au-PeEL)EBL5594480(OCoLC)1076256806(MiAaPQ)EBC6841918(Au-PeEL)EBL6841918(PPN)155218832(EXLCZ)99100000000043710220220906d1991 uy 0engurnn|008mamaatxtccrMathematical methods for hydrodynamic limits /Anna de Masi, Errico Presutti1st ed. 1991.Berlin, Germany ;New York, New York :Springer,[1991]©19911 online resource (VIII, 196 p.) Lecture Notes in Mathematics,0075-8434 ;1501Bibliographic Level Mode of Issuance: Monograph3-540-55004-6 Includes bibliographical references.Hydrodynamic limits for independent particles -- Hydrodynamics of the zero range process -- Particle models for reaction-diffusion equations -- Particle models for the Carleman equation -- The Glauber+Kawasaki process -- Hydrodynamic limits in kinetic models -- Phase separation and interface dynamics -- Escape from an unstable equilibrium -- Estimates on the V-functions.Entropy inequalities, correlation functions, couplings between stochastic processes are powerful techniques which have been extensively used to give arigorous foundation to the theory of complex, many component systems and to its many applications in a variety of fields as physics, biology, population dynamics, economics, ... The purpose of the book is to make theseand other mathematical methods accessible to readers with a limited background in probability and physics by examining in detail a few models where the techniques emerge clearly, while extra difficulties arekept to a minimum. Lanford's method and its extension to the hierarchy of equations for the truncated correlation functions, the v-functions, are presented and applied to prove the validity of macroscopic equations forstochastic particle systems which are perturbations of the independent and of the symmetric simple exclusion processes. Entropy inequalities are discussed in the frame of the Guo-Papanicolaou-Varadhan technique and of theKipnis-Olla-Varadhan super exponential estimates, with reference to zero-range models. Discrete velocity Boltzmann equations, reaction diffusion equations and non linear parabolic equations are considered, as limits of particles models. Phase separation phenomena are discussed in the context of Glauber+Kawasaki evolutions and reaction diffusion equations. Although the emphasis is onthe mathematical aspects, the physical motivations are explained through theanalysis of the single models, without attempting, however to survey the entire subject of hydrodynamical limits.Lecture notes in mathematics (Springer-Verlag) ;1501.Percolation (Statistical physics)Percolation (Statistical physics)530.13De Masi Anna1953-59538Presutti Errico1942-MiAaPQMiAaPQMiAaPQBOOK996466474403316Mathematical Methods for Hydrodynamic Limits382685UNISA