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008 121227s1991 gw | s |||| 0|eng d
020 _a9783540466369
_9978-3-540-46636-9
024 7 _a10.1007/BFb0086457
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aMAT029000
_2bisacsh
072 7 _aPBT
_2thema
072 7 _aPBWL
_2thema
082 0 4 _a519.2
_223
100 1 _aMasi, Anna De.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aMathematical Methods for Hydrodynamic Limits
_h[electronic resource] /
_cby Anna De Masi, Errico Presutti.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1991.
300 _aVIII, 196 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1501
505 0 _aHydrodynamic 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.
520 _aEntropy 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.
650 0 _aDistribution (Probability theory.
650 0 _aStatistical physics.
650 1 4 _aProbability Theory and Stochastic Processes.
_0http://scigraph.springernature.com/things/product-market-codes/M27004
650 2 4 _aComplex Systems.
_0http://scigraph.springernature.com/things/product-market-codes/P33000
650 2 4 _aStatistical Physics and Dynamical Systems.
_0http://scigraph.springernature.com/things/product-market-codes/P19090
700 1 _aPresutti, Errico.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662203255
776 0 8 _iPrinted edition:
_z9783540550044
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1501
856 4 0 _uhttps://doi.org/10.1007/BFb0086457
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c11112
_d11112